In a hydrogen like ionised atom, a single electron is orbiting around a stationary positive charge. If a spectral line of λ equal to 4861 A ∘ is observed due to transition from n = 12 to n = 6 . What is the wavelength of a spectral line due to transition from n = 9 to n = 6 and also identify the element?

Given, A spectral line of wavelength λ = 4861 × 10 - 10 m due to transition from n = 12 to n = 6 . As λ = h c ∆ E and if E 0 is the energy at ground state then ⇒ 4861 × 10 - 10 = h c E 0 1 6 2 - 1 12 2 ⇒ 4861 × 10 - 10 = 48 h c E 0 . . . 1 For a transition from n = 9 to n = 6 , ⇒ λ ' = h c E 0 1 6 2 - 1 9 2 ⇒ λ ' = 64 . 8 h c E 0 . . . 2 On dividing 2 by 1 λ ' 4861 × 10 - 10 = 64 . 8 48 ⇒ λ ' = 6563 × 10 - 10 m . From 1 , ⇒ E 0 = 48 h c 4861 × 10 - 10 eV = Z 2 × 13 . 6 eV ⇒ 48 × 6 . 626 × 10 - 34 × 3 × 10 8 4861 × 10 - 10 × 13 . 6 × 1 . 6 × 10 - 19 = Z 2 ⇒ Z 2 = 9 ⇒ Z = 3 .

Suppose the potential energy between electron and proton at a distance r is given by U = k e ln r a , where r < a and k , e , a are positive constants. Use Bohr’s theory to obtain the energy of nth energy level for such an atom.

Given, Potential energy, U = k e ln r a . Force, F = - d U d r ⇒ F = - d d r k e ln r a ⇒ F = - k e d d r ln r a ⇒ F = - k e r This force provides the centripetal acceleration on the orbiting electron. Thus, m v 2 r = k e r ⇒ v = k e m According to Bohr's theory, m v r = n h 2 π ⇒ r = n h 2 π m v = n h 2 π m k e m ⇒ r = n h 2 π k e m . Potential energy, U = k e ln 1 a n h 2 π k e m , Kinetic energy, K . E . = 1 2 m v 2 = k e 2 , Therefore, Total energy, E = U + K . E . ⇒ E = k e ln 1 a n h 2 π k e m + k e 2 ⇒ E = k e 2 1 + 2 ln 1 a n h 2 π k e m

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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 $13.6 eV$ .

Important Questions on Atomic Physics

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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.

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 7

In a hydrogen like ionised atom, a single electron is orbiting around a stationary positive charge. If a spectral line of

λ

equal to

4861 \overset{\circ}{A}

is observed due to transition from

n = 12

n = 6

. What is the wavelength of a spectral line due to transition from

n = 9

n = 6

and also identify the element?

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 8

An electron in the ground state of hydrogen atoms is revolving in anti clock wise direction in a circular orbit of radius $R$ .

Question Image

(i) Obtain an expression for the orbital magnetic dipole moment of the electron.
(ii) The atom is placed in a uniform magnetic induction, such that the plane normal to the electron orbit makes an angle of $30 °$ with the magnetic induction. Find the torque experienced by the orbiting electron.

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 9

A proton and an electron, both at rest initially, combine to form a hydrogen atom in the ground state. A single photon is emitted in this process. What is the wavelength?

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 10

A neutron of kinetic energy $65 eV$ collides inelastically with a singly ionized helium atom at rest. It is scattered at an angle of $90 °$ with respect of its original direction.

(a) Find the allowed values of the energy of the neutron and that of the atom after the collision.

(b) If the atom gets de-excited subsequently by emitting radiation, find the frequencies of the emitted radiation. [Given: Mass of $He$ atom = $4 \times$ (mass of neutrons Ionization energy of $H$ atom $= 13.6 eV$ ]

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 11

Suppose the potential energy between electron and proton at a distance

r

is given by

U = k e \ln (\frac{r}{a})

, where

r < a

and

k, e, a

are positive constants. Use Bohr’s theory to obtain the energy of nth energy level for such an atom.

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 12

A positronium consists of an electron and a positron revolving about their common centre of mass. Derive and calculate

(i) Separation between the electron and positron in their first excited state.

(ii) Kinetic energy of the electron in ground state.

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Alpha Question Bank for Engineering: Physics>Chapter 33 - Atomic Physics>Exercise - 4>Q 13

The

K_{β}

x -

ray of argon has a wavelength of

0.36 nm

. The minimum energy required to take out the outermost electron from argon atom is

16.53 eV

. Find the energy (in

KeV

) needed to knock out an electrons from the

K

shell of an argon.

Hydrogen atom in its ground state is excited by means of monochromatic radiation of wave length 975 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.

Important Questions on Atomic Physics

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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 $13.6 eV$ .