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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A diatomic molecule is made of two masses $m_{1}$ and $m_{2}$ which are separated by a distance $r$ . If we calculate its rotational energy by applying Bohr’s rule of angular momentum quantization, its energy will be given by : ( $n$ is an integer) $(h = \frac{h}{2 π})$

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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 23

In a hydrogen-like atom, electron makes the transition from an energy level with a quantum number

n

to another with quantum number

(n - 1) .

n > > 1

, the frequency of radiation emitted is proportional to :

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 3>Q 24

Hydrogen

(^{1} H_{1}),

Deuterium

(^{1} H_{2}),

singly ionised Helium

(_{2} {He}^{4})^{+}

and doubly ionised lithium

(_{3} {Li}^{6})^{+ +}

all have one electron around the nucleus. Consider an electron transition from

n = 2 to n = 1 .

If the wavelengths of emitted radiation are

λ_{1}, λ_{2}, λ_{3}, and λ_{4}

respectively then approximately which one of the following is correct?

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 3>Q 25

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion:

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 3>Q 26

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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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.

A diatomic molecule is made of two masses m1 and m2 which are separated by a distance r. If we calculate its rotational energy by applying Bohr’s rule of angular momentum quantization, its energy will be given by : (n is an integer) h=h2π

Important Questions on Atomic Physics

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A diatomic molecule is made of two masses $m_{1}$ and $m_{2}$ which are separated by a distance $r$ . If we calculate its rotational energy by applying Bohr’s rule of angular momentum quantization, its energy will be given by : ( $n$ is an integer) $(h = \frac{h}{2 π})$