Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 6

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Formula of De - Broglie Wavelength

Formula of De - Broglie Wavelength

Q: 15. What is the de Broglie wavelength of:

(A) A bullet of mass travelling at the speed of,

(B) A ball of mass moving at a speed of, and

(C) A dust particle of mass drifting with a speed of?

Answer:

(A)Mass of the bullet,

Speed of the bullet,

Planck’s constant,

De Broglie wavelength of the bullet is given by the relation:

(B) Mass of the ball,

Speed of the ball,

De Broglie wavelength of the ball is given by the relation:

(C)Mass of the dust particle,

Speed of the dust particle,

De Broglie wavelength of the dust particle is given by the relation:

Q: 16. An electron and a photon each have a wavelength of. Find

(A) Their momenta,

(B) The energy of the photon, and

(C) The kinetic energy of electron.

Answer:

Wavelength of an electron and a photon

Planck’s constant,

(A) The momentum of an elementary particle is given by de Broglie relation:

It is clear that momentum depends only on the wavelength of the particle. Since the wavelengths of an electron and a photon are equal, both have an equal momentum.

(B) The energy of a photon is given by the relation:

Where,

Speed of light,

Therefore, the energy of the photon is.

(C) The kinetic energy (K) of an electron having momentum, is given by the relation:

Where,

Mass of the electron

Hence, the kinetic energy of the electron is.