Atoms

Class 12

8 previous-year questions from this chapter every option and the correct answer, free · where the marks are

1. Rutherford and Bohr models

Exam focus: Rutherford's model correctly located the nucleus but couldn't explain atomic stability — classically an accelerating orbiting electron should radiate energy and spiral inward. Bohr fixed exactly this by allowing only orbits with quantised angular momentum, L = nh/2π.

Bohr's Atomic Model: Postulates, Formulae and Derivations

Physics Wallah - Alakh Pandey

Part 2 of a series (part 1 separately covers Rutherford's alpha-scattering model); covers Bohr's postulates and derivations thoroughly but Rutherford's model itself is only lead-in context here.

PhysicsNEET 2025show ▾

A particle of mass

m

is moving around the origin with a constant force

F

pulling it towards the origin. If the Bohr model is used to describe its motion, the radius of the

n

th orbit and the particle's speed

v

in the orbit depend on

n

as:

A. $r \propto n^{1/3}; v \propto n^{1/3}$
B. $r \propto n^{1/3}; v \propto n^{2/3}$
C. $r \propto n^{2/3}; v \propto n^{1/3}$ ✓
D. $r \propto n^{4/3}; v \propto n^{- 1/3}$

Solution

Constant force $F = \frac{m v ^{2}}{r}$ and Bohr quantisation $m v r = \frac{nh}{2 π}$ . From the first, $v^{2} \propto r$ ; substituting, $r^{3/2} \propto n \Rightarrow r \propto n^{2/3}$ and $v \propto r^{1/2} \propto n^{1/3}$ .

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PhysicsNEET 2024show ▾

Given below are two statements: Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their characteristic spectrum. In the light of the above statements, choose the most appropriate answer from the options given below:

A.Both Statement I and Statement II are incorrect
B.Statement I is correct but Statement II is incorrect✓
C.Statement I is incorrect but Statement II is correct
D.Both Statement I and Statement II are correct

Solution

Atoms are neutral because they carry equal positive and negative charge — Statement I is correct. Atoms emit their characteristic spectrum only when excited, not simply because they are stable — Statement II is incorrect.

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PhysicsNEET 2023show ▾

The radius of the innermost orbit of the hydrogen atom is

5.3 \times 1 0^{- 11}

m. What is the radius of the third allowed orbit of the hydrogen atom?

A.0.53 Å
B.1.06 Å
C.1.59 Å
D.4.77 Å✓

The worked solution is part of a paid pack.

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PhysicsNEET 2020show ▾

For which one of the following is the Bohr model not valid?

A.Hydrogen atom
B.Singly ionised helium atom ( $H e^{+}$ )
C.Deuteron atom
D.Singly ionised neon atom ( $N e^{+}$ )✓

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2. Hydrogen spectrum and energy levels

Exam focus: Only the Balmer series lands substantially in the visible range, since it ends at n=2 — Lyman (ending at n=1) is entirely ultraviolet and the rest are infrared. Energy levels En = −13.6/n² eV are always negative, approaching zero only at ionisation.

Atomic Spectrum: Lyman, Balmer Series and Energy Levels

Physics Wallah - Alakh Pandey

Dedicated lecture on emission/absorption spectra and the hydrogen spectral series.

PhysicsNEET 2024show ▾

Match List I with List II.

List I (Spectral lines of hydrogen for transitions from)	List II (Wavelength, nm)
A. $n_{2} = 3$ to $n_{1} = 2$	I. 410.2
B. $n_{2} = 4$ to $n_{1} = 2$	II. 434.1
C. $n_{2} = 5$ to $n_{1} = 2$	III. 656.3
D. $n_{2} = 6$ to $n_{1} = 2$	IV. 486.1

Choose the correct answer from the options given below:

A.A-III, B-IV, C-II, D-I✓
B.A-IV, B-III, C-I, D-II
C.A-I, B-II, C-III, D-IV
D.A-II, B-I, C-IV, D-III

Solution

Balmer wavelengths follow $\frac{1}{λ} \propto (\frac{1}{4} - \frac{1}{n ^{2}})$ : the smallest jump ( $n = 3 \to 2$ ) gives the longest wavelength, 656.3 nm $(H - α)$ , then 486.1, 434.1 and 410.2 nm as $n$ rises. Hence A-III, B-IV, C-II, D-I.