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(a) Using the Bohr’s model calculate the speed of the electron i...

(a) Using the Bohr’s model calcula | Class 12 Physics Chapter Atoms, Atoms NCERT Solutions

Welcome to the NCERT Solutions for Class 12 Physics - Chapter Atoms. This page offers a step-by-step solution to the specific question from Exercise 1, Question 7: . With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.

Question 7:

(a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels.

(b) Calculate the orbital period in each of these levels.

Answer:

(a) Let ν₁ be the orbital speed of the electron in a hydrogen atom in the ground state level, n₁ = 1. For charge (e) of an electron, ν₁ is given by the relation,

ν₁ = e²/n₁4πϵ₀(h/2π) = e²/2ϵ₀h

Where, e = 1.6 × 10⁻¹⁹ C

ϵ₀ = Permittivity of free space = 8.85 × 10^-12 N⁻¹ C² m⁻²

h = Planck’s constant = 6.62 × 10⁻³⁴ Js

∴ ν₁ = (1.6x10^-19)2/2x8.85x10^-12x6.62x10^-34 = 0.0218 x 10⁸ = 2.18 x 10⁶ m/s

For level n₂ = 2, we can write the relation for the corresponding orbital speed as:

ν₂ = e²/n₂2ϵ₀h = (1.6x10^-19)2/2x2x8.85x10^-12x6.62x10^-34 = 1.09 x 10⁶ m/s

And, for n₃ = 3, we can write the relation for the corresponding orbital speed as:

ν₃ = e²/n₃2ϵ₀h = (1.6x10^-19)2/3x2x8.85x10^-12x6.62x10^-34 = 7.27 x 10⁵ m/s

Hence, the speed of the electron in a hydrogen atom in n = 1, n=2, and n=3 is 2.18 × 10 ⁶ m/s, 1.09 × 10 ⁶ m/s, 7.27 × 10 ⁵ m/s respectively.

(b) Let T ₁ be the orbital period of the electron when it is in level n₁ = 1.

Orbital period is related to orbital speed as:

T₁ = 2πr₁/ν₁

Where, r₁ = Radius of the orbit

= n₁²h²ϵ₀/πme²

h = Planck’s constant = 6.62 × 10⁻³⁴ Js

e = Charge on an electron = 1.6 × 10⁻¹⁹ C

ϵ₀ = Permittivity of free space = 8.85 × 10⁻¹² N⁻¹ C² m⁻²

m = Mass of an electron = 9.1 × 10⁻³¹ kg

∴ T₁ = 2πr₁/ν ₁

= (2πx(1)²x(6.62x10^-34)2x8.85x10^-12)/2.18x10⁶xπx9.1x10^-31x(1.6x10^-19)²

= 15.27x10^-17 = 1.527x10^-16 s

For level n ₂ = 2, we can write the period as:

T₂ = 2πr₂/ν ₂

Where, r₂ = Radius of the electron in n₂ = 2

= (n₂)²h²ϵ₀/πme²

∴ T₂ = 2πr₂/ν₂

= (2πx(2)²x(6.62x10^-34)²x8.85x10^-12)/1.09 x 10⁶ x π x 9.1 x 10^-31 x (1.6 x 10^-19)²

= 1.22 x 10^-15 s

And, for level n₃ = 3, we can write the period as:

T₃ = 2πr₃/ν ₃

Where, r ₃ = Radius of the electron in n₃ = 3

= (n₃)²h²ϵ₀/πme²

∴ T₃ = 2πr₃/ν ₃

= (2πx(3)²x(6.62x10^-34)2x8.85x10^-12)/7.27 x 10⁵ x π x 9.1 x 10^-31 x (1.6 x 10^-19)²

= 4.12 x 10^-15 s

Hence, the orbital period in each of these levels is 1.52 × 10 ⁻¹⁶ s, 1.22 × 10 ⁻¹⁵ s, and 4.12 × 10 ⁻¹⁵ s respectively.

Other Questions of Chapter Atoms

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1.5 × 10¹¹ m with orbital speed 3 × 10⁴ m/s. (Mass of earth = 6.0 × 10²⁴ kg.)

What is the shortest wavelength present in the Paschen series of spectral lines?

The ground state energy of hydrogen atom is −13.6 eV. What are the kinetic and potential energies of the electron in this state?

Q: Choose the correct alternative from the clues given at the end of the each statement:
(a) The size of the atom in Thomsons model is .......... the atomic size in Rutherfords model. (much greater than/no different from/much less than.)
(b) In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force. (Thomsons model/ Rutherfords model.)
(c) A classical atom based on .......... is doomed to collapse. (Thomsons model/ Rutherfords model.)
(d) An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in .......... (Thomsons model/ Rutherfords model.)
(e) The positively charged part of the atom possesses most of the mass in .......... (Rutherfords model/both the models.)

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

The radius of the innermost electron orbit of a hydrogen atom is 5.3 ×10 ⁻¹¹ m. What are the radii of the n = 2 and n =3 orbits?

Popular questions of class 12 Physics

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(a) Estimate the number of electrons transferred (from which to which?)

(b) Is there a transfer of mass from wool to polythene?

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Recently Viewed Questions of Class 12 Physics

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(a) Three resistors 2 Ω, 4 Ω and 5 Ω are combined in parallel. What is the total resistance of the combination?

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Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Atoms.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

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