# Physics Questions and Answers – Bohr Model of the Hydrogen Atom

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This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Bohr Model of the Hydrogen Atom”.

1. The radius of the Bohr orbit depends on which of the following?
a) $$\frac {1}{n }$$
b) n
c) $$\frac {1}{n^2}$$
d) n2

Explanation: The equation is given as:
rn = $$\frac {n^2h^2}{4\pi^2mkZe^2}$$.
From this, we can understand that rn is directly proportional to n2.

2. What is the order of the radius of an electron orbit in a hydrogen atom?
a) 10-8 m
b) 10-9 m
c) 10-11 m
d) 10-13 m

Explanation: The radius of an electron orbit in a hydrogen atom is of the order of 10-11 m. It is equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state.

3. What will be the longest wavelength in the Balmer series of hydrogen spectrum?
a) 6557 × 10-10 m
b) 5557 × 10-10 m
c) 9557 × 10-10 m
d) 1557 × 10-10 m

Explanation: $$\frac {1}{\lambda }$$ = R $$[ \frac {1}{n_1^2} – \frac {1}{n_2^2} ]$$
$$\frac {1}{\lambda }$$ = 1.098 × 107 $$[ \frac {1}{2^2} – \frac {1}{3^2} ]$$
λ = 36 × $$\frac {10^{-7}}{5}$$ × 1.098
λ = 6557 × 10-10 m.

4. A hydrogen atom in its ground state absorbs 10.2 eV of energy. What is the orbital angular momentum is increased by?
a) 4.22 × 10-3 Js
b) 2.11 × 10-34 Js
c) 3.16 × 10-34 Js
d) 1.05 × 10-34 Js

Explanation: Increase in angular momentum = $$\frac {h}{2π}$$.
$$\frac {h}{2π}$$ = 6.6 × $$\frac {10^{-34}}{2}$$ × 3.14
$$\frac {h}{2π}$$ = 1.05 × 10-34 Js.

5. Which of the following is true regarding the Bohr model of atoms?
a) Assumes that the angular momentum of electrons is quantized
c) Predicts continuous emission spectra for atoms
d) Predicts the same emission spectra for all types of atoms

Explanation: Bohr model of atoms assumes that the angular momentum of electrons is quantized. The atom is held between the nucleus and surroundings by electrostatic forces. The other options are not valid.

6. In terms of Bohr radius a0, the radius of the second Bohr orbit of a hydrogen atom is given by √2 a0.
a) True
b) False

Explanation: The equation is given as:
rn = r1 n2
r2 = (2)2r0 = 4r0. Thus, in terms of Bohr radius a0, the radius of the second Bohr orbit of a hydrogen atom is given by 4 a0.

7. Hydrogen atoms are excited from ground state to the state of principal quantum number 4. Then, what will be the number of spectral lines observed?
a) 3
b) 6
c) 5
d) 2

Explanation: n = 4.
The number of spectral lines emitted = $$\frac {n(n-1)}{2}$$.
$$\frac {n (n-1)}{2} = \frac {(4 \times 3)}{6}$$ = 2

8. When a hydrogen atom is in its first excited level, what is the relation of radius and Bohr radius?
a) Twice
b) 4 times
c) Same
d) Half

Explanation: For the first excited level, n = 2.
r2 = (2)2r0 = 4r0.
So, when a hydrogen atom is in its first excited level, its radius is 4 times of the Bohr radius.

Sanfoundry Global Education & Learning Series – Physics – Class 12. 