Suppose the potential energy between electron & proton at a distance r is given by - k e 2 3 r 3 . Use Bohr’s theory to obtain energy levels of such a hypothetical hydrogen atom.

Given, Potential energy, U = - k e 2 3 r 3 The electrostatic force between electron and proton at a distance r is given by, F = - d U d r = k e 2 r 4 . According to Bohr's first postulate, m v 2 r = k e 2 r 4 ...( 1 ) According to Bohr's second postulate, m v r = n h 2 π ...( 2 ) From equation ( 1 ) and ( 2 ), r = 4 π 2 e 2 k m n 2 h 2 The total energy of the electron, E = K + U = 1 2 m v 2 − k e 2 3 r 3 = k e 2 2 r 3 − k e 2 3 r 3 (from equ. 1 ) ⇒ E = k e 2 6 r 3 Substituting the value of r , we get: E = n 6 h 6 384 m 3 K 2 e 4 π 6

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Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r = \frac{λ_{1}}{λ_{2}},$ is given by :

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Important Questions on Atomic Physics

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 3>Q 27

If the series limit frequency of the Lyman series is

ν_{L},

then the series limit frequency of the Pfund series is:

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 3>Q 28

An electron from various excited states of hydrogen atom emits radiation to come to the ground state. Let

λ_{n}, λ_{g}

be the de-Broglie wavelength of the electron in the

n^{th}

state and the ground state respectively. Let

\land_{n}

be the wavelength of the emitted photon in transition from the

n^{th}

state to the ground state. For large

n,

(A, B are constants)

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 1

A small particle of mass

m

moves in such a way that the potential energy

U = \frac{1}{2} m b^{2} r^{2}

, where

b

is a constant and

r

is the distance of the particle from the origin (Nucleus). Assuming Bohr model of quantization of angular momentum and circular orbits, show that the radius of the

n^{th}

allowed orbit is proportional to

n

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 2

Suppose the potential energy between electron & proton at a distance

r

is given by

\frac{- k e^{2}}{3 r^{3}}

. Use Bohr’s theory to obtain energy levels of such a hypothetical hydrogen atom.

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 3

Suppose in certain conditions only those transitions are allowed to hydrogen atoms in which the principal quantum number $n$ change by $2$ .

(i) Find the smallest wavelength emitted by hydrogen

(ii) List the wavelengths emitted by hydrogen in the visible range ( $380 nm$ to $780 nm$ ) ( $h = 4.14 \times 10^{- 15} eV s & c = 3 \times 10^{8} m s^{- 1}$ )

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 4

A beam of monochromatic light of wavelength

λ

ejects photoelectrons from a caesium surface

(ϕ = 1.9 eV)

These photoelectrons are made to collide with hydrogen atoms in ground state .Find the maximum value of

λ

for which (a) hydrogen atoms may be ionised (b) hydrogen atoms may get excited from the ground state to the first excited state and (c) the excited hydrogen atoms may emit visible light.

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 5

Hydrogen atom in its ground state is excited by means of monochromatic radiation of wave length

975 \dot{A}

. How many different lines are possible in the resulting spectrum? Calculate the longest wavelength among them. You may assume the ionization energy of hydrogen atom as

13.6 eV

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 6

Average lifetime of a hydrogen atom excited to

n = 2

state is

10^{- 8} s

. Find the number of revolutions made by the electrons on the average before it jumps to the ground state.

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = λ1λ2, is given by :

Important Questions on Atomic Physics

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Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r = \frac{λ_{1}}{λ_{2}},$ is given by :