LEARNING CLOSE TO YOU

Choose your location

Use a city to find schools, tutors, educators and learning support. You can change it anytime.

With your permission, your browser shares your coordinates with Google to find your city.

LoginSign Up

CLASS 12 · PHYSICS · CHAPTER 12

Atoms

Student-friendly answers to all nine exercises on atomic models and the Bohr model of hydrogen.

9 worked answersComplete chapter answers
Read the NCERT questions ↗← All chapters

9 worked answers · short steps first, explanations when you need them

Chapter 12 Exercises

Textbook pages 305

Question 1

Choose the correct alternatives: (a) Is an atom's size in Thomson's model much greater than, the same order as, or much less than in Rutherford's model? (b) In which model are electrons in stable equilibrium, and in which do they experience a net force? (c) Which classical model predicts an atom will collapse? (d) Which model has nearly continuous mass distribution, and which has highly non-uniform mass distribution? (e) In which model(s) does the positively charged part contain most of the atom's mass?

Steps only

Thomson: atom's size is the same order, electrons can be in equilibrium, and positive mass/charge is spread through the atom. Rutherford: electrons feel nuclear attraction, a classical orbit would collapse, and mass is concentrated in a tiny nucleus.

Answer

(a) Same order; (b) Thomson, then Rutherford; (c) Rutherford; (d) Thomson, then Rutherford; (e) both.

Question 2

Suppose the alpha-particle scattering experiment is repeated with a thin sheet of solid hydrogen instead of gold foil. What results would you expect?

Steps only

Hydrogen nuclei have charge +e (not +79e) and are much lighter than alpha particles. They recoil, and they repel alpha particles less strongly than gold nuclei do.

Answer

Expect mostly forward-moving alpha particles and recoiling protons, with no frequent large-angle/backward scattering.

Question 3

Two energy levels in an atom differ by 2.3 eV. Find the frequency of radiation emitted when the atom changes from the higher level to the lower level.

Steps only

ν=ΔE/h=(2.3×1.602×10⁻¹⁹)/(6.626×10⁻³⁴)=5.56×10¹⁴ Hz.

Answer

5.6×10¹⁴ Hz.

Question 4

The ground-state energy of a hydrogen atom is −13.6 eV. Find the kinetic and potential energies of its electron.

Steps only

For a Coulomb-bound electron, K=−E=13.6 eV and U=2E=−27.2 eV.

Answer

K=13.6 eV; U=−27.2 eV.

Question 5

A hydrogen atom in its ground state absorbs a photon and reaches the n=4 level. Find the photon's wavelength and frequency.

Steps only

ΔE=−0.85−(−13.6)=12.75 eV; ν=ΔE/h=3.09×10¹⁵ Hz; λ=c/ν=97.2 nm.

Answer

97.2 nm; 3.09×10¹⁵ Hz.

Question 6

Using Bohr's model, find (a) the electron speed and (b) the orbital period in the n=1, 2, and 3 levels of hydrogen.

Steps only

vₙ=2.18×10⁶/n m/s; Tₙ=2πrₙ/vₙ=n³(1.53×10⁻¹⁶ s).

Answer

n=1: 2.18×10⁶ m/s, 1.53×10⁻¹⁶ s; n=2: 1.09×10⁶ m/s, 1.22×10⁻¹⁵ s; n=3: 7.27×10⁵ m/s, 4.13×10⁻¹⁵ s.

Question 7

The radius of hydrogen's innermost electron orbit is 5.3×10⁻¹¹ m. Find the radii of the n=2 and n=3 orbits.

Steps only

rₙ=n²r₁: r₂=4r₁=2.12×10⁻¹⁰ m; r₃=9r₁=4.77×10⁻¹⁰ m.

Answer

2.12×10⁻¹⁰ m; 4.77×10⁻¹⁰ m.

Question 8

A 12.5 eV electron beam bombards hydrogen gas at room temperature. What series of wavelengths will be emitted?

Steps only

12.5 eV can excite ground-state hydrogen to n=2 or n=3, but not n=4. The possible decays are 2→1, 3→1 and 3→2.

Rydberg formula gives 121.6 nm, 102.6 nm, and 656.3 nm.

Answer

Lyman-α 121.6 nm; Lyman-β 102.6 nm; Balmer-α 656.3 nm.

Question 9

In Bohr's model, estimate the quantum number for Earth orbiting the Sun at radius 1.5×10¹¹ m with speed 3×10⁴ m/s. Use Earth's mass 6.0×10²⁴ kg.

Steps only

n=2πmvr/h=2π(6.0×10²⁴)(3.0×10⁴)(1.5×10¹¹)/(6.626×10⁻³⁴)≈2.6×10⁷⁴.

Answer

n≈2.6×10⁷⁴.

WE’RE HERE TO HELP

How can we help?

Looking for a special educator, a tutor, or learning support? Send us your query.