Prasanna

You can Download Chapter 10 Consumption And Investment Function Questions and Answers, Notes, 2nd PUC Economics Question Bank with Answers Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Economics Question Bank Chapter 10 Consumption And Investment Function

2nd PUC Economics Consumption And Investment Function One Mark Questions and Answers

Question 1.
Write the meaning of consumption.
Answer:
Consumption refers to using of goods and services to attain desired satisfaction. It also represents the total quantity of products bought and used by consumers during a particular period of time.

Question 2.
What to do you mean by savings?
Answer:
Savings refer to the excess of income over expenditure.

Question 3.
Define investment.
Answer:
According to J.M.Keynes, investment refers to an addition to the nation’s physical stock of capital goods like roads, bridges, buildings, machines etc.

Question 4.
What is MPC?
Answer:
MPC (Marginal Propensity to Consume) refers to the ratio of change in consumption to the change in income.

where ∆c refers to change in consumption and ∆y refers to change in the income of the consumer.

Question 5.
Give the meaning of Multiplier.
Answer:
Multiplier is the ratio of the total change in income to the initial change in investment. It expresses the quantitative relationship between increase in income and increase in investment.

Question 6.
What is APC?
Answer:
APC – Average Propensity to Consume is the ratio of consumption expenditure to income in a given period of time. APC = C/Y where C is consumption and Y is income.

Question 7.
How do you calculate MPS?
Answer:
The Marginal Propensity to save (MPS) is obtained as follows:
MPS = 1 – MPC.

2nd PUC Economics Consumption And Investment Function Two Marks Questions and Answers

Question 1.
Define Income as per J.M. Keynes.
Answer:
According to J.M.Keynes, Income refers to total money remuneration received by four factors of production in the form of rent, wages, interest and profit. It is expressed as follows:
Y = C + I where, Y is income, C is consumption expenditure and ‘I’ investment expenditure.

Question 2.
How is saving equal to investment?
Answer:
The equality between saving and investment is through the mechanism of rate of interest. If the saving is more than investment, the rate of interest falls, investment increases and savings comes down. When the saving is less than investment, rate of interest increases and investment comes down and the savings gets increased to the level of investment.

According to Keynes, Y = C + S and Y = C + I, therefore C + S = C + I, so S = I
Y-income, C-consumption, S-savings, I-investment.

Question 3.
State the factors which influence Marginal Propensity to Consume(MPC).
Answer:
There are two main factors which affect the Marginal Propensity to Consume viz., Subjective factors and Objective factors. The subjective factors include psychological characters of human beings, social practices and institutions etc. The objective factors include, change in the wage level, changes in fiscal policy, change in expectations, change in rate of interest etc.

Question 4.
Briefly explain the relationship between multiplier and MPC.
Answer:
The effect of multiplier depends on Marginal propensity to consume as its value is determined by MPC alone. If MPC is higher, multiplier will also be higher. The multiplier can be calculated by the following formula:

Question 5.
Differentiate between autonomous and induced investments.
Answer:

Autonomous Investment	Induced Investment
(i) It is independent of the level of income.	(i) It is profit or income motivated.
(ii) It is influenced by innovations, growth of population, social and legal institutions etc.	(ii) It is made by the people as a result of change in income.
(iii) It is income inelastic	(iii) It is income elastic

Question 6.
Mention any four types of investments.
Answer:
The types of investments are as follows:

1. Private Investment and Public Investment.
2. Induced Investment and Autonomous Investment.
3. Ex-ante Investment (Planned) and Ex-post Investment (unplanned).
4. Gross Investment and Net Investment.

2nd PUC Economics Consumption And Investment Function Five Marks Questions and Answers

Question 1.
What is investment? Briefly explain the various types of investment.
Answer:
According to J.M.Keynes, investment refers to an addition to the nation’s physical stock of capital goods like roads, bridges, buildings, machines etc.

The types of investment are as follows:
1. Private Investment and Public Investment: Private investment is that investment which is undertaken by private individuals, enterprises, industrialists etc. Public investments are those investments which are made by Government authorities. The intention of private investment is profit and public investment is social benefits.

2. Induced Investment and Autonomous Investment: Induced investment is made by the people as a result of change in their income level. It is profit or income motivated. So, it is income elastic. The autonomous investment is public investment which is independent of the level of income. It is income inelastic. It is influenced by innovations, growth of population, social and legal institutions etc.

3. Ex-ante Investment and Ex-post Investment: Ex-ante investment is that investment which is actually planned according to objectives and investment is made. This investment is planned in advance. The ex-post investment is that investment which cannot be planned in advance. It is that investment which arises instantly during the course of production process.

4.  Gross Investment and Net Investment: Gross investment is the total value of the asset made or created. It includes buildings, dams, roads, railways, industries, etc. The net investment is obtained by deducting depreciation from Gross Investment.

Question 2.
Explain the J.M.Keynes consumption function in brief.
Answer:
The consumption function also called as propensity to consume refers to income consumption relationship. It is a functional relationship between Total consumption and Gross national income. The consumption function may be represented as follows:
C = f (Y). where C is consumption, Y is income and f is die functional relationship.

In fact, consumption function is a schedule of the various amounts of consumption expenditure corresponding to different levels of income. The following table shows the imaginary consumption schedule:

Income (Y) in crores	Consumption(C) in crores.
0	30
50	60
120	120
180	160
240	200
300	240
360	280

The above table shows that the consumption is an increasing function of income because consumption expenditure increases with increase in income. When the income is zero, people spend out of their past savings on consumption because they must eat to live. When income is 50 crores, it is still not sufficient to meet the consumption expenditure of the community as the consumption expenditure (Rs. 60) is more than the income (Rs. 50).

When the income is equal to 120 crores the consumption is also Rs. 120 crores. After this stage, income is shown to increase by 60 crores (240 – 180) and the consumption goes up by only 40 crores (160 -120). This implies that increase in consumption is less than the corresponding increase in income.

In the above diagram, income is measured horizontally and consumption is measured vertically. 45 degree is the unity line where at all levels income and consumption are equal. The C curve is a linear consumption function based on the assumption that consumption changes by the same amount. Its upward slope to the right indicates that consumption is an increasing function of income.

B is the break-even point where C = Y or OY₁ = OC₁. When income rises to OY₂, consumption also increases to OC₂, but the increase in consumption is less than the increase in income, CC₁ <  Y₁ Y₂. The portion of income not consumed is saved and represented as SS₁.

Question 3.
Explain the investment function of Keynes in brief.
Answer:
Generally, investment means buying shares, stocks, bonds, securities existing in stock market. According to J.M.Keynes, investment refers to real investment which adds to capital stock. It leads to increase in level of income and production by increasing the production and purchase of capital goods.

Investment is the production or acquisition of real capital assets during any period of time. Capital and investment are related to each other through net investment. As the income of the community increases, consumption also increases. But, it does not increase in the same proportion. There will be a gap between income and consumption. The gap must be filled by increasing employment and production. For this, investment is needed.

The decision to invest in a new capital asset depends on whether the expected rate of return on the new investment is equal to or greater or less than the rate of interest to be paid on the funds needed to purchase this asset. It is only when the expected rate of return is higher than the interest rate that investment will be made in acquiring new capital assets.

In reality, there are three factors that are taken into consideration while making any investment decision.
They are as follows:

1. The cost of capital asset.
2. The expected rate of returns during its lifetime.
3. Market rate of interest.

Question 4.
Explain the concept of Multiplier of Keynes.
Answer:
According to Keynes, Multiplier establishes a precise relationship, given the propensity to consume, between aggregate employment and income and the rate of investment. It tells us that, when there is an increment of investment, income will increase by an amount which is K times the increment of investment. It can be expressed as follows:
K = ∆Y/∆I, where ∆Y is the change in income and ∆I is the change in investment and K is the multiplier.

Problem: If the investment increases from Rs.1000 crores to Rs.1500 crores, income may increase from Rs.2000 to Rs.3000 crores, then find the multiplier.

In the multiplier theory, the important element is the multiplier coefficient, K which refers to the power by which any initial investment expenditure is multiplied to obtain a final increase in income. The value of multiplier is determined by the MPC. The higher the rate of MPC, the higher is the value of multiplier and vice versa.

The effect of multiplier depends on Marginal propensity to consume as its value is determined by MPC alone. If MPC is higher, multiplier will also be higher. The multiplier can be calculated by the following formula:
If MPC is deducted from I, we get MPS i.e., Marginal Propensity to Save. Now the above formula becomes as follows:

If MPC is deducted from I, we get MPS i.e., Marginal Propensity to Save. Now the above formula becomes as follows:

Working of Multiplier: Multiplier works both forward and backward. In forward working, an increase in investment leads to increased production which creates income and generates consumption expenditure. This process continues in dwindling series till no further increase in income and expenditure is possible.

In backward operation, the multiplier operates backward. A reduction in investment will lead to contraction of income and consumption which, in turn, will lead to cumulative decline in income and consumption till the contraction in aggregate income is the multiple of the initial decrease in investment.

The size of multiplier varies directly with the size of the MPC. The working of multiplier can be illustrated with the help of the following diagram:

In the above diagram, the original investment is I.I (OI) and the original income is OY. S…S is the saving curve. The two curves intersect at point E. If there is an increase in investment, then the I..I curve will shift to a position above the earlier level to I,…I. Now, curves I,..I, and S..S intersect at point E₁ and the new level of income OY₁ is determined. This emphasizes the fact that an initial increase in investment leads to a large increase in income.

Question 5.
What is Multiplier? What is its importance?
Answer:
According to J.M. Keynes, Multiplier establishes a precise relationship, given the propensity to consume, between aggregate employment and income and the rate of investment. It tells us that, when there is an increment of investment, income will increase by an amount which is K times the increment of investment. It can be expressed as follows:
K = ∆Y/∆I, where ∆Y is change in income and ∆I is Change in investment and K is the multiplier.

The concept of multiplier is an important contribution of Keynes to the theory of income, output and employment.
The importance of multiplier is as follows:

• The theory of multiplier highlights the importance of investment in income and employment theory.
• The multiplier throws a spotlight on the different phases of the business cycles.
• It helps in bringing equality between saving and investment.
• It is an important tool in formulating economic policies.
• It provides guidelines to achieve full employment.
• It highlights the importance of deficit financing (Public expenditure greater than public revenue).
• It points out the role of public investment in economic development.

2nd PUC Economics Consumption And Investment Function Ten Marks Questions and Answers

Question 1.
Explain the concepts of saving and investment. Discuss the equality between saving and investment.
Answer:
The consumption function also called as propensity to consume refers to income consumption relationship. It is functional relationship between Total consumption and Gross national income. The consumption function may be represented as follow.

C = f (Y). where C is consumption, Y is income and f is the functional relationship.

In fact, consumption function is a schedule of the various amounts of consumption expenditure corresponding to different levels of income.

(a) Investment function:
Generally, investment means buying shares, stocks, bonds, securities existing in stock market. According to J.M.Keynes, investment refers to real investment which adds to capital stock It leads to increase in level of income and production by increasing the production and purchase of capital goods.

Investment is the production or acquisition of real capital assets during any period of time. Capital and investment are related to each other through net investment. As the income of the community increases, consumption also increases. But, it does not increase in the same proportion. There will be a gap between income and consumption. This gap must be filled by increasing employment and production. For this, investment is needed.

The decision to invest in a new capital asset depends on whether the expected rate of return on the new investment is equal to or greater or less than the rate of interest to be paid on the funds needed to purchase this asset. It is only when the expected rate of return is higher than the interest rate that investment will be made in acquiring new capital assets.

In reality, there are three factors that are taken into consideration while making any investment decision. They are as follows:

1. The cost of capital asset.
2. The expected rate of returns during its lifetime.
3. Market rate of interest.

(b) Equality between saving and investment:
The equality between saving and investment is through the mechanism of rate of interest. If the saving is more than investment, the rate of interest falls, investment increases and saving comes down. When the saving is less than investment, rate of interest increases and investment comes down and the savings gets increased to the level of investment.

According to Keynes, Y = C + S and Y = C + I, therefore C + S = C + I, so S = I
Y-income, C-consumption, S-saving, I-investment.

Question 2.
Explain Keynes consumption function. Discuss the properties of consumption function.
Answer:
The consumption function also called as propensity to consume refers to income consumption relationship. It is a functional relationship between Total consumption and Gross national income. The consumption function may be represented as follows:
C = f (Y). where C is consumption, Y is income and f is the functional relationship.

In fact, consumption function is a schedule of the various amounts of consumption expenditure corresponding to different levels of income. The following table shows the imaginary consumption schedule:

Income (Y) in crores	Consumption(C) in crores
0	30
50	60
120	120
180	160
240	200
300	240
360	280

The above table shows that the consumption is an increasing function of income because consumption expenditure increases with increase in income. When the income is zero, people spend out of their past savings on consumption because they must eat to live. When income is is 50 crores, it is still not sufficient to meet the consumption expenditure of the community which at 60 crores is more than the income. When the income is equal to 120 crores which is the basic consumption level. After this stage, income is shown to increase by 60 crores and the consumption goes up by only 40 crores. This implies that increase in consumption is less than the corresponding increase in income.

In the above diagram, income is measured horizontally and consumption is measured vertically.. 45 degree is the unity line where at all levels income and consumption are equal. The C curve is a linear consumption function based on the assumption that consumption changes by the same amount. Its upward slope to the right indicates that consumption is an increasing function of income. B is the break-even point where C = Y.

When income rises to OC₂, consumption also increases to OY₂, but the increase in consumption is less than the increase in income, C₁C₂ < Y₁Y₂. The portion of income not consumed is saved and is represented as SS₁.

Question 3.
What do you mean by investment function? Discuss the types and determinants of investment.
Answer:
Generally, investment means buying shares, stocks, bonds, securities existing in stock market. According to J.M.Keynes, investment refers to real investment which adds to capital stock. It leads to increase in level of income and production by increasing the production and purchase of capital goods.

Investment is the production or acquisition of real capital assets during any period of time. Capital and investment are related to each other through net investment. As the income of the community increases, consumption also increases. But, it does not increase in the same proportion. There will be a gap between income and consumption. This gap must be filled by increasing employment and production. For this, investment is needed.

The decision to invest in a new capital asset depends on whether the expected rate of return on the new investment is equal to or greater or less than the rate of interest to be paid on the funds needed to purchase this asset. It is only when the expected rate of return is higher than the interest rate that investment will be made in acquiring new capital assets.

In reality, there are three factors that are taken into consideration while making any investment decision. They are as follows:

1. The cost of capital asset.
2. The expected rate of returns during its lifetime.
3. Market rate of interest.

The types of investment are as follows:
1. Private Investment and Public Investment: Private investment is that investment which is undertaken by private individuals, enterprises, industrialists etc. Public investments are those investments which are made by Government authorities. The intention of private investment is profit and public investment is social benefits.

2. Induced Investment and Autonomous Investment: Induced investment is made by the people as a result of change in their income level. It is profit or income motivated. So, it is income elastic. The autonomous investment is public investment which is independent of the level of income. It is income inelastic. It is influenced by innovations, growth of population, social and legal institutions etc.

3. Ex-ante Investment and Ex-post Investment: Ex-ante investment is that investment which is actually planned according to objectives and investment is made. This investment is planned in advance. The ex-post investment is that investment which cannot be planned in advance. It is that investment which arises instantly during the course of production process.

4. Gross Investment and Net Investment: Gross investment is the total value of the asset made or created. It includes buildings, dams, roads, railways, industries, etc. The net investment is obtained by deducting depreciation from Gross Investment.

Determinants of Investments:
The investment depends on two factors viz., Marginal efficiency of Capital and rate of interest.
a) Marginal Efficiency of Capital (MEC): The MEC is the highest rate of returns expected from an additional unit of a capital asset over its cost. According to Kurihara “ MEC is the ratio between the prospective yield of additional capital goods and their supply price”. The prospective yield is the aggregate net returns from an asset during its lifetime, while the supply price is the cost of producing the asset.

If the supply price of a capital asset is Rs.20;000 and its annual yield is Rs.2,000, the Marginal Efficiency of this asset is 2000/20000 x 100/1 = 10%. The MEC is the percentage of profit expected from a given investment on a capital asset.

b) Rate of Interest: The investment is also determined by the rate of interest. If the rate of interest is higher, the investment will be low as MEC becomes less. If the MEC is higher than the rate of interest, there will be a tendency to borrow funds in order to invest in new capital assets. If the MEC is lower than the rate of interest, no firm will borrow to invest in capital assets. Thus the equilibrium condition for a firm to hold the optimum capital stock is where the MEC is equal to the interest rate.

You can Download Chapter 12 Atoms Questions and Answers, Notes, 2nd PUC Physics Question Bank with Answers, Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Physics Question Bank Chapter 12 Atoms

2nd PUC Physics Atoms NCERT Text Book Questions and Answers

Question 1.
Choose the correct alternative from the clues given at the end of each statement:

1. The size of the atom in Thomson’s model is ………….. the atomic size in Rutherford’s model, (much greater than/ no different from/much less than.)
2. In the ground state of …………..electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson’s model/ Rutherford’s model.)
3. A classical atom based on ………….. is doomed to collapse. (Thomson’s model/ Rutherford’s model.)
4. An atom has a nearly continuous mass distribution in a ………….. but has a highly non-uniform mass distribution in (Thomson’s model/ Rutherford’s model.)
5. The positively charged part of the atom possesses most of the mass in ………….. (Rutherford’s model/both the models.)

Answer:

1. No different from
2. Thomson’s model, Rutherford’s model
3. Rutherford’s model
4. Thomson’s model, Rutherford’s model
5. both the models.

Question 2
Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?
Answer:
α-particle is much heavier than hydrogen nuclei. Therefore, α-particles pass through solid hydrogen without deflection. In other words, α-particles are not scattered by solid hydrogen.

Question 3.
What is the shortest wavelength present in the Paschen series of spectral lines?
Answer:
The wavelengths of the spectral lines in the Paschen series are given by

Question 4.
A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level?
Answer:

Question 5.
The ground state energy of the hydrogen atom is -13.6 eV. What are the kinetic and potential energies Of the electron in this state?
Answer:
The kinetic energy of the electron in an orbit is numerically equal to its total energy. Therefore, the kinetic energy of the electron = 13.6 eV
The potential energy of the electron in an orbit is equal to twice, its total energy
= -13.6 ×2
= -27.2 eV.

Question 6.
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.
Answer:
The energy of the electron in the ground state
E_e = -13.6 eV
Also, the energy of the electron in n=4 level,

Question 7.
(a) Using Bohr’s model calculates the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels,
(b) Calculate the orbital period in each of these levels.
Answer:
(a) The speed of an electron in the n^th orbit of an H-atom is given by

From equation (i), it follows that the velocity of electron in an orbit of a hydrogen atom is inversely proportional to its quantum number (n).

(b) The orbital period of an electron in the n^th orbit of an H-atom is given by

It follows that orbital period of an electron in H-atom is directly proportional to the cube of its quantum number.

Question 8.
The radius of the innermost electron orbit of a hydrogen atom is 5.3 x 10^-11. What are the radii of the n = 2 and n = 3 orbits?
Answer:
The radius of an orbit in a hydrogen atom is directly proportional to the square of its quantum number i.e.

Question 9.
A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
Answer:
The first, second and third excited energies for hydrogen atom are
E’ ₁ = E₂ – E₁ = -3.4 – [-13.6] = 10.2 eV,
E’₂ = E₃ – E₁= -1.51 – [-13.6] = 12.09 eV,
and E’₃ = E₄ – E₁ = -0.85 – [-13.6] = 12.75 eV
It follows that when a 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature, the H – atoms at the most will be raised to n = 3 level. The H – atoms may come to ground state directly or via n = 2 level. Therefore, the wavelengths emitted will lie in Balmer series [for de-excitation from n = 3 level to n = 2 and 1 level] and Lyman series [for de­excitation from n = 2 level to n = 1 level].

Question 10.
In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius  1.5 x 10¹¹ m with orbital speed 3 x 10⁴ m/s. (Mass of earth = 6.0 x 10²⁴)
Answer:
Here, m = 6.0 x 10²⁴ kg; r = 1.5×10ⁿm
and v = 3 x 10⁴ ms^-1
The angular momentum of the earth,
mvr = 6.0×10²⁴ x 3 x 10⁴ x 1.5 x 10¹¹ = 2.7 x 10⁴⁰ kg ms^-1 
In accordance with Bohr’s model

2nd PUC Physics Atoms Additional Exercise

Question 11.
Answer the following questions, which help you understand the difference between Thomson’s model and Rutherford’s model better.

(a) Is the average angle of deflection of α-particles by a thin gold foil predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?

(b) Is the probability of backward scattering (i.e., scattering of α-particles at angles greater than 90°) predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?

(c) Keeping other factors fixed, it is found experimentally that for small thickness t, the number of α-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?

(d) In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of a -particles by a thin foil?

Answer:
(a) Is the average angle of deflection of α-particles by a thin gold foil predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?

(b) Is the probability of backward scattering (i.e., scattering of α-particles at angles greater than 90°) predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?

(c) Keeping other factors fixed, it is found experimentally that for small thickness t, the number of α-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?

(d) In which model is it completely wrong to ignore multiple scattering for the calculation of the average angle of scattering of a -particles by a thin foil?

Question 12.
The gravitational attraction between electron and proton in a hydrogen atom is weaker than the Coulomb attraction by a factor of about 10^-40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.
Answer:
Let m and m be the masses of electron and proton respectively. If the electron and proton were bound only by gravitational attraction, then

According to Bohr’s quantization conditions, the angular momentum of the electron.

Question 13.
Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n-1). For large n, show that this frequency equals the classical frequency of revolution of the electron in the orbit.
Answer:
When a hydrogen atom de-excites from level n₁ to n_p the frequency of radiation emitted is given by


Hence, when n is large, the frequency of radiation emitted is equal to the classical frequency of revolution of the electron in the orbit.

Question 14.
Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, a thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learned in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10^-10m).

(a) Construct a quantity with the dimensions of length from the fundamental constants e, m_e, and c. Determine its numerical value.

(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, m_e, and e and confirm that its numerical value has indeed the correct order of magnitude.
Answer:
(a) The quantity with the dimensions of length constructed from the fundamental constants e, m, and c is

(b) The quantity with the dimensions of length constructed from the fundamental constants h, e, and m is the radius of the innermost orbit (n = 1) of the H – atom. It is given by,

It is also called Bohr’s radius
Substituting the values of h, m_e and 4π∈_o in equation (1),

Question 15.
The total energy of an electron in the first excited state of the hydrogen atom is about -3.4 eV.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is changed?
Answer:
We know that K.E and P.E of the electron in the n^th energy state of the hydrogen atom are respectively given by

The first excited state corresponds to n = 2 level.
Now, the total energy of an electron in
n = 2 state is given to be – 3.4 eV.

(a) Therefore, K.E of the electron in the first excited state (n = 2) of the hydrogen atom

(b) E of the electron in the first excited state (n = 2) of the hydrogen atom.

(c) If the zero of potential energy is chosen differently, K.E does not change. The P.E and total energy will change

Question 16.
If Bohr’s quantisation postulate (angular momentum = nh/2π) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbits of planets around the sun?
Answer:
The mass of a planet is very large as compared to that of electron and accordingly, its angular momentum is very large. For \(\frac { h }{ 2\pi } \) example, in terms of the angular, from the
Bohr’s quantisation relation,\(\frac { nh }{ 2\pi } \) it follows that for the orbital motion of the earth, n = 10⁷⁰. For such a large value of n, the difference in the energies of the successive energy levels are so small as compared to the energies associated with the energy levels that these levels form an energy continuum, i.e the levels appear to be continuous.

Question  17.
Obtain the first Bohr’s radius and the ground state energy of a muonic hydrogen atom [i.e., an atom in which a negatively charged muon (μ^–) of mass about 207m_e orbits around a proton].
Answer:
Let m be the mass of the electron. the firest Bohr radius of H- atom is given by,

in a muonic hydrogen atom, in place of an electron, a negatively charged muon having mass 207 m. revolves around the nucleus of hydrogen i.e. proton.
If r₁‘ is first Bohr’s radius of muonic hydrogen atom,

2nd PUC Physics Atoms Additional Questions and Answers

Question 1.
What is the ratio of radii of the orbits corresponding to first excited state and ground state of hydrogen atom?
Answer:
The radius of the n^th orbit, r_n α n²
The ground state corresponds to n = 1 and the
a first excited state corresponds to n = 2

Question 2.
The ground state energy of the hydrogen atom is -13.6eV. What are the kinetic and potential energies of the electron in this state?
Answer:
The potential energy (E_p) of the electron in an orbit is equal to twice its total energy (E) = -13.6 x 2 = -27.2eV
The kinetic energy (E_k) of the electron in an orbit is equal to the negative of its total energy (E) = E_k – E = -(-13.6) = 13.6 eV.

Question 3.
The radius of 1st electron orbit of hydrogen atom is 5.3 x 10^-11 m. What is the radius of 2^nd orbit?
Answer:

Question 4.
What is energy possessed by an electron in n = ∞ ?
Answer:
Energy of electron in n^th orbit of a hydrogen atom is given by

Question 5.
If 13.6eV energy is required to ionise the hydrogen atom, then the energy required to remove an electron from n = 2 is
(A) 2 eV
(B) 0 eV
(C) 3.4 eV
(D) 6.8 eV
Answer:
Required energy

Question 6.
The transition from state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in transition from
(A) n = 2  to  n = 1
(B) n = 3 to n = 2
(C) n = 4  to n = 2
(D) n = 5 to n = 4
Answer:
Infrared region lies for the Bracket series, i.e. the transition from n = 5 to n = 4.

Question 7.
Which of the following transition in a hydrogen atom emits the photon of highest frequency?
(A) n = 2 to  n = 6
(B) n   = 2 to n =   1
(C) n = 6  to    n = 2
(D) n   = 1 to n =   2
Answer:
\(v={ R }_{ c }\left( \frac { 1 }{ { n }_{ i }^{ 2 } } -\frac { 1 }{ { n }_{ f }^{ 2 } } \right) \)
Substituting various values of n and n_p it is observed, maximum frequency is obtained for transition from n = 2 to n = 1.

Question 8.
When a hydrogen atom is raised from ground to excited state,
(A) The P.E increases and K.E decreases
(B) The P.E decreases and K.E increases
(c) Both P.E and K.E increase
(d) Both P.E and K.E decreases
Answer:
(B) The P.E decreases and K.E increases

Question 9.
In which of these, will radius of first orbit be minimum?
(A) H atom
(B) ²₁H atom
(C) He⁺ ion
(D) Li²⁺ ion
Answer:

Question 10.
The minimum wavelength of the x-rays produced by electrons accelerated through a potential difference of V(volt) is directly proportional to
(A) \(\sqrt { v } \)
(B) \({ v }^{ 2 }\)
(C) \(\frac { 1 }{ \sqrt { v } } \)
(D) \(\frac { 1 }{ v } \)
Answer:
(D) \(\frac { 1 }{ v } \)