This set of Engineering Physics Multiple Choice Questions & Answers (MCQs) focuses on “Einstein Coefficients”.

1. Which of the following is the correct expression for the relation between Einstein’s coefficients A and B?

a) \(\frac{8\pi v^3 h}{c^3}\)

b) \(\frac{8\pi v^2 h}{c^3}\)

c) \(\frac{8\pi v^2 h}{c^2}\)

d) \(\frac{8\pi hv}{c^3}\)

View Answer

Explanation: The expression \(\frac{8\pi v^3 h}{c^3}\) is the correct expression for the relation between the two Einstein’s coefficients. This expression is known as the Einstein’s relation.

2. What is the relationship between B_{21} and B_{12}?

a) B_{12} > B_{21}

b) B_{12} < B_{21}

c) B_{12} = B_{21}

d) No specific relation

View Answer

Explanation: B

_{21}is the coefficient for the stimulated emission while B

_{12}is the coefficient for stimulated absorption. Both the processes are mutually reverse processes and their probabilities are equal. Therefore, B

_{12}= B

_{21}.

3. Which of the following Einstein’s coefficient represents spontaneous emission?

a) A_{12}

b) A_{21}

c) B_{12}

d) B_{21}

View Answer

Explanation: A

_{21}represents the spontaneous emission of photons. A

_{12}signifies spontaneous absorption.B

_{12}is for stimulated absorption while B

_{21}is for stimulated emission.

4. The correct expression for the rate of stimulated emission is _______________

a) R_{se} = A_{21}N_{2}

b) R_{se} = A_{21}uN_{2}

c) R_{se} = B_{21}N_{2}

d) R_{se} = B_{21}uN_{2}

View Answer

Explanation: The stimulates emission is directly proportional to the energy density u, of the external radiation field. Also, stimulated emission rate increases with the increase in number N

_{2}of exited atoms.

5. Which law is used for achieving the relation between the Einstein’s coefficients?

a) Heisenberg’s Uncertainty Principle

b) Planck’s radiation law

c) Einstein’s equation

d) Quantum law

View Answer

Explanation: Planck’s radiation law, which gives the energy density u = \(\frac{8πhv^3}{c^3} \frac{1}{e^α-1}\), is used as the formula resembles the one for the energy density of the external radiation field in stimulated emission, u = \(\frac{A_{21}}{B_{21}(\frac{B_{12}}{B_{21}}e^α-1)}\).

6. The probability of spontaneous emission increases rapidly with the energy difference between the two states.

a) True

b) False

View Answer

Explanation: From Einstein’s relation we know that the ratio of Einstein’s coefficients is \(\frac{8\pi v^3 h}{c^3}\). Thus, the ration of Einstein’s coefficients is proportional to the cube of the frequency. Hence, the probability of spontaneous emission increases rapidly with the energy difference between the two states.

7. If the frequency of emitted photon is 10 Hz, the ratio of Einstein’s coefficient is _____________

a) 2.177 X 10^{-51}

b) 3.177 X 10^{-51}

c) 5.177 X 10^{-51}

d) 6.177 X 10^{-51}

View Answer

Explanation: We know Einstein’s relation = \(\frac{8\pi v^3 h}{c^3}\)

v = 10 Hz, h = 6.63 X 10

^{-34}Js, c = 3 X 10

^{8}m/s

Therefore, the ratio of Einstein’s coefficients is: 6.177 X 10

^{-51}.

8. What is the unit of the coefficient of spontaneous emission?

a) s^{-1}

b) s

c) J^{-1}

d) J

View Answer

Explanation: For spontaneous emission, the expression for the rate is = A

_{21}N

_{2}, where N

_{2}is the number of particles in exited state. As the unit of rate is Number of particles per second, the unit of A

_{21}is s

^{-1}.

9. What is the unit for the coefficient of stimulated emission?

a) s^{-2}

b) m^{3} s^{-2}

c) J^{−1} m^{3}

d) J^{−1} m^{3} s^{-2}

View Answer

Explanation: For stimulated emission, the expression for the rate is B

_{21}uN

_{2}where u stands for the energy density and N is the number of exited atoms. Therefore, the unit of B turns out to be J

^{−1}m

^{3}s

^{-2}.

10. Which Einstein’s coefficient should be used in this case?

a) A_{12}

b) A_{21}

c) B_{12}

d) B_{21}

View Answer

Explanation: The given figure shows stimulated emission. Hence, the Einstein coefficient for stimulated emission is B

_{21}. If it had been spontaneous emission, then A

_{21}would have been used.

**Sanfoundry Global Education & Learning Series – Engineering Physics.**

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