Check Here the Most Important Questions of Quantum Mechanics! (Download PDF)

Quantum Mechanics - Most Important Questions! (Download PDF)

1. For an H-atom, how much energy is needed to remove an electron from the n = 8 state of a hydrogen atom?

1. -0.32 eV
2. -0.21 eV
3. -4.32 eV
4. None of the above

2. Calculate the maximum wavelength that hydrogen in its ground state can absorb. What would be the next smallest wavelength that would work?

1. 122 nm,103 nm
2. 120 nm, 110 nm
3. 130 nm, 103 nm
4. 90 nm, 103 nm

3. A microscope using suitable photons is used to locate an electron in an atom within a distance of . Determine the uncertainty involved in the measurement of its velocity? (h = 6.626 × 10^-34 Js, mass of electron = 9.1 × 10^-31 kg).

1. 5.79×10⁵ m/s
2. 5.79×10⁴ m/s
3. 5.79×10⁶ m/s
4. 5.79×10⁷ m/s

4. A cricket ball has a weight of 100 g is located within 1 nm. Determine the uncertainty in the velocity.

1. 5.27×10^-23 m/s
2. 5.27×10^-25 m/s
3. 5.27×10^-24 m/s
4. 5.27×10^-27 m/s

5. Calculate the wavelength of light emitted when the electron in a hydrogen atom undergoes a transition from an energy level with n = 4 to an energy level with n = 2.

1. 500 nm
2. 684 nm
3. 486 nm
4. 328 nm

6. The function N₁(a² – x²) is defined for the interval x = -a to x = +a. Determine the value of N₁.

1. 3/2a
2. 15/4a^5/2
3. √5/2a^3/2
4. None of the above.

7. An electron is confined in a 1- D box having a length of 1 Å. If an electron falls from an excited state to a ground state, what energy it will emit?

1. 120.8 eV
2. 112.8 eV
3. 210.7 eV
4. 320.8 eV

8. An electron confined to a one-dimensional box of length 0.14 nm has a ground-state energy corresponding to the radiation of wavelength about 70 nm. Benzene, as a rough approximation, maybe a two-dimensional box that encompasses the regular hexagonal shape. The C-C bond length in benzene is 0.14 nm due to which side of the box would be about 0.28 nm. Estimate wavelength for the transition from the ground state to the first excited state of benzene, assuming that it is π-bonding electrons that are involved. 

1. 100 nm
2. 93 nm
3. 87 nm
4. 78 nm

9. The wave function of a state of the hydrogen atom is:

Here, denotes the normalized eigenfunction of the state with quantum numbers n, l and m in the usual notation. Calculate the expectation value of L_z in the state  .

10. Given the usual canonical commutation relations, the commutator [A, B] of A = i(xp_y – yp_x) and B = (yp_z + zp_y) is :

ANSWER KEYS

1. B
2. A
3. C
4. B
5. C
6. B
7. B
8. B
9. D
10. D

Solutions

 Solution 1:

For H-atom, the expression of energy in eV is:

    E= -13.6 eV/n²

        = -13.6 eV/64

        = -0.21 eV

 Solution 2:

 Solution 3:

 Solution 4:

 Solution 5:

 Solution 6:

 Solution 7:

 Solution 8:

 Solution 9:

 Solution 10:

Download Important Questions on Quantum Mechanics - Download PDF Here

Check Out: 

• Study Notes for CSIR NET Life Science - (Download PDF)
• Study Notes for CSIR NET Chemical Science - Download PDF Here!

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