Atoms

part 1

Atomic Models

• Thomson's atomic model
• Rutherford's alpha particle scattering experiment
• Rutherford's nuclear model of atom
• Limitations of Rutherford model

part 2

Bohr's Model

• Bohr's postulates
• Bohr's model of hydrogen atom
• Energy levels and radii of hydrogen atom
• Hydrogen spectrum — spectral series

part 3

Energy Levels and Spectra

• Line spectra of hydrogen — Lyman, Balmer, Paschen series
• Energy of electron in nth orbit
• de Broglie explanation of Bohr quantisation
• Limitations of Bohr model

Bohr's radius of nth orbit

$r_n = \frac{n^2 a_0}{Z}$ (a₀ = 0.529 Å)

★ board favourite

Energy of electron in nth orbit

$E_n = -\frac{13.6 Z^2}{n^2}$ eV

★ board favourite

Rydberg formula

$\frac{1}{\lambda} = RZ^2\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$ [R = 1.097×10⁷ m⁻¹]

★ board favourite

Velocity in nth orbit

$v_n = \frac{2.18\times10^6 Z}{n}$ m/s

★ frequently asked

Frequency of emitted photon

$h\nu = E_2 - E_1$ (E₂ > E₁)

★ frequently asked

Bohr's angular momentum condition

$mvr = \frac{nh}{2\pi} = n\hbar$

★ frequently asked

Name the spectral series of hydrogen that lies in (i) the ultraviolet and (ii) the visible region. Using the Rydberg formula, find the wavelength of the first line of the Balmer series. (R = 1.097×10⁷ m⁻¹)

What is the ratio of the radii of the orbits corresponding to n = 1 and n = 3 in a hydrogen atom?

State Bohr's postulates for the hydrogen atom. Using them, derive expressions for (a) radius of nth orbit, (b) velocity of electron in nth orbit, (c) total energy of electron in nth orbit.

The ground state energy of hydrogen is −13.6 eV. What is the energy of the electron in the n = 2 state? What is the energy required to ionise a hydrogen atom from its ground state?

Explain the origin of spectral lines in hydrogen. An electron in hydrogen jumps from n=4 to n=2. Calculate the wavelength of radiation emitted (R_H = 1.097×10⁷ m⁻¹).

In the Rutherford scattering experiment, why do only a very small number of alpha particles get deflected through large angles?

Using Bohr's postulates, derive the expression for the total energy of an electron in the nth stationary orbit of a hydrogen atom. Why is the total energy negative?

State Bohr's quantisation condition for the angular momentum of an electron in a stationary orbit. Show that the de Broglie hypothesis leads to the same condition.

How many marks is Atoms worth in the Class 12 board exam?

Around 4 marks of the 70-mark CBSE Physics theory paper, based on the official unit-wise weightage. Bohr's model and hydrogen spectrum lines — mostly conceptual.

Is Atoms easy or hard?

It's rated medium — a moderate-difficulty chapter in Class 12 Physics. Most students need about 3 hours to cover it well.

What are the important topics in Atoms?

The chapter covers 10 NCERT topics in 3 areas: Atomic Models; Bohr's Model; Energy Levels and Spectra.

What questions come from Atoms in board exams?

Between 2018–2024, CBSE board papers asked questions from this chapter on Spectral Series, Bohr's Model, Energy Levels, Hydrogen Spectrum — 1- to 5-mark questions.