Bohr's Model & Energy Levels — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Bohr's Model & Energy Levels MCQs with step-by-step solutions (21 questions). Part of Structure of Atoms and Nuclei. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Bohr's Model & Energy Levels · easy · theory
According to Bohr's postulate, the orbital angular momentum of an electron in the $n^{\text{th}}$ orbit is:
A. $\dfrac{n^2h}{2\pi}$
B. $\dfrac{h}{2\pi n}$
C. $\dfrac{2\pi n}{h}$
D. $\dfrac{nh}{2\pi}$ ✓ Correct
Solution: Only orbits satisfying this quantisation condition are allowed.
Q2 — Bohr's Model & Energy Levels · easy · theory
According to Bohr's model, an electron revolving in a stationary orbit:
A. Radiates energy continuously
B. Does not radiate energy ✓ Correct
C. Absorbs energy continuously
D. Loses mass steadily
Solution: This postulate was introduced precisely to rescue the atom from classical collapse.
Q3 — Bohr's Model & Energy Levels · easy · theory
Radiation is emitted by an atom when an electron:
A. Jumps from a lower level to a higher one
B. Jumps from a higher energy level to a lower one ✓ Correct
C. Leaves the atom entirely
D. Remains in a stationary orbit
Solution: The photon energy is exactly the difference between the two levels, $h\nu = E_2 - E_1$.
Q4 — Bohr's Model & Energy Levels · medium · theory
In the Bohr model of hydrogen, the radius of the $n^{\text{th}}$ orbit varies as:
A. $\dfrac{1}{n}$
B. $n^2$ ✓ Correct
C. $\dfrac{1}{n^2}$
D. $n$
Solution: The orbits therefore spread out rapidly: the second is four times the first, the third nine times.
Q5 — Bohr's Model & Energy Levels · medium · theory
In the Bohr model, the energy of the $n^{\text{th}}$ level varies as:
A. $-n$
B. $-n^2$
C. $-\dfrac{1}{n}$
D. $-\dfrac{1}{n^2}$ ✓ Correct
Solution: The levels crowd together as $n$ increases, converging on zero at ionisation.
Q6 — Bohr's Model & Energy Levels · medium · theory
The orbital speed of the electron in the $n^{\text{th}}$ Bohr orbit varies as:
A. $\dfrac{1}{n^2}$
B. $n$
C. $\dfrac{1}{n}$ ✓ Correct
D. $n^2$
Solution: Electrons in outer orbits move more slowly as well as further out.
Q7 — Bohr's Model & Energy Levels · easy · theory
The radius of the first Bohr orbit of hydrogen is approximately:
A. $0.053\text{ \AA}$
B. $1.06\text{ \AA}$
C. $0.53\text{ \AA}$ ✓ Correct
D. $5.3\text{ \AA}$
Solution: This value, $5.3 \times 10^{-11}\text{ m}$, is known as the Bohr radius.
Q8 — Bohr's Model & Energy Levels · easy · theory
The energy of the electron in the ground state of hydrogen is:
A. $-27.2\text{ eV}$
B. $+13.6\text{ eV}$
C. $-3.4\text{ eV}$
D. $-13.6\text{ eV}$ ✓ Correct
Solution: The negative sign indicates that the electron is bound to the nucleus.
Q9 — Bohr's Model & Energy Levels · hard · theory
For an electron in a Bohr orbit, the kinetic energy and the total energy are related by:
A. $K = -\dfrac{E}{2}$
B. $K = E$
C. $K = -E$ ✓ Correct
D. $K = 2E$
Solution: The potential energy is $2E$, so the kinetic energy is $-E$ and their sum is $E$.
Q10 — Bohr's Model & Energy Levels · easy · numerical
The radius of the first Bohr orbit of hydrogen is $r_0$. The radius of the third orbit is:
A. $9r_0$ ✓ Correct
B. $3r_0$
C. $6r_0$
D. $\dfrac{r_0}{9}$
Solution: $r_n \propto n^2$, so $r_3 = 9r_0$.
Q11 — Bohr's Model & Energy Levels · medium · numerical
The total energy of an electron in the second excited state ($n = 3$) of hydrogen is:
A. $-1.51\text{ eV}$ ✓ Correct
B. $-13.6\text{ eV}$
C. $-3.4\text{ eV}$
D. $-0.85\text{ eV}$
Solution: $E_n = -\dfrac{13.6}{n^2} = -\dfrac{13.6}{9} \approx -1.51\text{ eV}$.
Q12 — Bohr's Model & Energy Levels · easy · numerical
The energy of an electron in the first excited state ($n = 2$) of hydrogen is:
A. $-6.8\text{ eV}$
B. $-3.4\text{ eV}$ ✓ Correct
C. $-1.51\text{ eV}$
D. $-13.6\text{ eV}$
Solution: $E_2 = -\dfrac{13.6}{4} = -3.4\text{ eV}$.
Q13 — Bohr's Model & Energy Levels · hard · numerical
The ratio of the kinetic energy to the total energy of an electron in any Bohr orbit is:
A. $+1$
B. $-1$ ✓ Correct
C. $+2$
D. $-2$
Solution: Since $E = -K$, the ratio $\dfrac{K}{E} = -1$.
Q14 — Bohr's Model & Energy Levels · hard · numerical
The total energy of an electron in the ground state of hydrogen is $-13.6\text{ eV}$. Its kinetic and potential energies are respectively:
A. $-13.6\text{ eV}$ and $-13.6\text{ eV}$
B. $+13.6\text{ eV}$ and $-27.2\text{ eV}$ ✓ Correct
C. $-13.6\text{ eV}$ and $+27.2\text{ eV}$
D. $+13.6\text{ eV}$ and $+13.6\text{ eV}$
Solution: $K = -E = +13.6\text{ eV}$ and $U = 2E = -27.2\text{ eV}$; their sum is $-13.6\text{ eV}$.
Q15 — Bohr's Model & Energy Levels · medium · numerical
The radius of the second Bohr orbit of hydrogen is approximately:
A. $0.53\text{ \AA}$
B. $1.06\text{ \AA}$
C. $4.77\text{ \AA}$
D. $2.12\text{ \AA}$ ✓ Correct
Solution: $r_2 = 4 \times 0.53 = 2.12\text{ \AA}$.
Q16 — Bohr's Model & Energy Levels · medium · numerical
If the speed of the electron in the first Bohr orbit is $v_1$, its speed in the second orbit is:
A. $\dfrac{v_1}{2}$ ✓ Correct
B. $2v_1$
C. $\dfrac{v_1}{4}$
D. $4v_1$
Solution: $v_n \propto \dfrac{1}{n}$.
Q17 — Bohr's Model & Energy Levels · medium · numerical
The energy of an electron in the $n = 4$ level of hydrogen is:
A. $-0.54\text{ eV}$
B. $-1.51\text{ eV}$
C. $-0.85\text{ eV}$ ✓ Correct
D. $-3.4\text{ eV}$
Solution: $E_4 = -\dfrac{13.6}{16} = -0.85\text{ eV}$.
Q18 — Bohr's Model & Energy Levels · easy · numerical
The energy required to ionise a hydrogen atom from its ground state is:
A. $3.4\text{ eV}$
B. $27.2\text{ eV}$
C. $13.6\text{ eV}$ ✓ Correct
D. $10.2\text{ eV}$
Solution: Ionisation means raising the electron from $-13.6\text{ eV}$ to zero energy.
Q19 — Bohr's Model & Energy Levels · medium · numerical
The angular momentum of an electron in the second Bohr orbit is:
A. $\dfrac{h}{\pi}$ ✓ Correct
B. $\dfrac{h}{4\pi}$
C. $\dfrac{h}{2\pi}$
D. $\dfrac{2h}{\pi}$
Solution: $L = \dfrac{nh}{2\pi} = \dfrac{2h}{2\pi} = \dfrac{h}{\pi}$.
Q20 — Bohr's Model & Energy Levels · medium · numerical
The energy of an electron in the $n = 5$ level of hydrogen is approximately:
A. $-2.72\text{ eV}$
B. $-0.54\text{ eV}$ ✓ Correct
C. $-0.85\text{ eV}$
D. $-1.51\text{ eV}$
Solution: $E_5 = -\dfrac{13.6}{25} = -0.544\text{ eV}$.
Q21 — Bohr's Model & Energy Levels · medium · numerical
The radius of the fourth Bohr orbit of hydrogen is approximately:
A. $0.53\text{ \AA}$
B. $2.12\text{ \AA}$
C. $8.48\text{ \AA}$ ✓ Correct
D. $4.24\text{ \AA}$
Solution: $r_4 = 16 \times 0.53 = 8.48\text{ \AA}$.