For what kinetic energy of a neutron will the associated de Broglie wavelength be 1 . 40 × 10 - 10 m ? The mass of a neutron is 1 . 675 × 10 - 27 kg and h = 6 . 63 × 10 - 34 Js .

Given, De-Broglie wavelength of the neutron = 1 . 40 × 10 - 10 m . Planck’s constant h = 6 . 63 × 10 - 34 Js . Mass of neutron m n = 1 . 675 × 10 − 27 kg . Kinetic energy (K) and velocity (v) are related as K = 1 2 m n v 2 . . . . . . . . . . . . 1 De-Broglie wavelength λ and velocity v are related as: λ = h m n v . . . . . . . . . . . . 2 Using eq (2) in eq (1), we get, K = 1 2 m n h 2 λ 2 m n 2 = h 2 2 λ 2 m n = 6 . 63 × 10 - 34 2 2 × 1 . 40 × 10 - 10 2 × 1 . 66 × 10 - 27 = 6 . 75 × 10 - 21 J = 6 . 75 × 10 - 21 1 . 6 × 10 - 19 = 4 . 219 × 10 - 2 eV Therefor the kinetic energy of the neutron is 6 . 75 × 10 - 21 J or 4 . 219 × 10 - 2 eV . Hence, it is the required answer.

The combination of fundamental quantities e 2 2 ε 0 hc ≡ α is known as the fine structure constant. Show that α is a pure number, of magnitude 1 137

α = e 2 2 ε 0 c h (Given) ⇒ α = 1 . 6 × 10 - 19 2 2 × 8 . 85 × 10 - 12 × 3 × 10 8 × 6 . 63 × 10 - 34 ⇒ α = 1 137 Simply it is coupling constant or measure the strength of electromagnetic force that govern how electrically charged elementary (electron, muon) and photon interact.

What is rest mass of photon?

By nature, photons are just energy packets which are travelling continuously. Therefore photons have zero rest mass as they are never stationary. Note-According to Einstein's quantum theory light propagates in the form of packets i.e. quanta of energy, which is called photon. The rest mass of photons is being zero. It can be shown, according to the relativity theory of light. According to the relativistic theory equation, the mass of the photon is computed as: m = m 0 1 − ( c 2 / v 2 ) m 0 = m 1 − ( c 2 / v 2 ) when v = 0 ; So m 0 = 0 Where m 0 is the rest mass of the Photon .

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Earn 100

Using the Rydberg formula, calculate the wavelength of the first four spectral lines in the Balmer series of the hydrogen spectrum.

Important Questions on Bohr Model, X-Ray Spectra, Wave-Particle Duality

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12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 20 - Bohr Model, X-Ray Spectra, Wave-Particle Duality>EXERCISE 20>Q 8

The energy of an electron in an excited hydrogen atom is

- 3.4 eV

. Calculate the angular momentum of the electron according to Bohr's theory. Planck's constant

h = 6.626 \times 10^{- 34} Js

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12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 20 - Bohr Model, X-Ray Spectra, Wave-Particle Duality>EXERCISE 20>Q 9

In a hydrogen atom, a transition takes place from

n = 3

n = 2

orbit. Calculate the wavelength of the emitted photon. Will the photon be visible? To which spectral series will this photon belong?

(R = 1.097 \times 10^{7} m^{- 1})

HARD

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IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 20 - Bohr Model, X-Ray Spectra, Wave-Particle Duality>EXERCISE 20>Q 10

Find the recoil speed of a hydrogen atom after it emits a photon in going from

n = 5

state to

n = 1

state. Given

R = 1.097 \times 10^{7} m^{- 1}, h = 6.63 \times 10^{- 34}

and mass of hydrogen atom,

m_{H} = 1.67 \times 10^{- 27} kg

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12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 20 - Bohr Model, X-Ray Spectra, Wave-Particle Duality>EXERCISE 20>Q 11

Calculate the de-Broglie wavelength of a proton of kinetic energy

500 eV

. The mass of proton is

1.67 \times 10^{- 27} kg (h = 6.63 \times 10^{- 34} Js and 1 eV = 1.6 \times 10^{- 19} J)

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12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 20 - Bohr Model, X-Ray Spectra, Wave-Particle Duality>EXERCISE 20>Q 12

For what kinetic energy of a neutron will the associated de Broglie wavelength be

1.40 \times 10^{- 10} m

? The mass of a neutron is

1.675 \times 10^{- 27} kg

and

h = 6.63 \times 10^{- 34} Js

EASY

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 20 - Bohr Model, X-Ray Spectra, Wave-Particle Duality>EXERCISE 20>Q 13

The combination of fundamental quantities

\frac{e^{2}}{2 ε_{0} hc} \equiv α

is known as the fine structure constant. Show that

α

is a pure number, of magnitude

\frac{1}{137}

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12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 20 - Bohr Model, X-Ray Spectra, Wave-Particle Duality>EXERCISE 20>Q 14

A gas of monoatomic hydrogen is bombarded with a stream of electrons that have been accelerated from rest through a potential difference of

12.75 V

. Which spectral lines should be emitted ?

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IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 20 - Bohr Model, X-Ray Spectra, Wave-Particle Duality>EXERCISE 20>Q 15

In a hydrogen atom, electron moves from second excited state to first excited state and then from the first excited state to the ground state. Find the ratio of the wavelengths obtained.

Using the Rydberg formula, calculate the wavelength of the first four spectral lines in the Balmer series of the hydrogen spectrum.

Important Questions on Bohr Model, X-Ray Spectra, Wave-Particle Duality

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