Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 5

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De Broglie Hypothesis

De Broglie Hypothesis

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Q: 13. What is the

(A) Momentum,

(B) Speed, and

(C) de Broglie wavelength of an electron with kinetic energy of.

Answer:

Kinetic energy of the electron,

Planck’s constant,

Mass of an electron,

Charge on an electron,

(A) For the electron, we can write the relation for kinetic energy as:

Where,

Speed of the electron

Momentum of the electron,

Therefore, the momentum of the electron is .

(B) Speed of the electron,

(C) De Broglie wavelength of an electron having a momentum, is given as:

Therefore, the de Broglie wavelength of the electron is .

Q: 14. The wavelength of light from the spectral emission line of sodium is . Find the kinetic energy at which

(A) An electron, and

(B) A neutron, would have the same de Broglie wavelength.

Answer:

Wavelength of light of a sodium line,

Mass of an electron,

Mass of a neutron,

Planck’s constant,

(A) For the kinetic energy K, of an electron accelerating with a velocity v, we have the relation:

We have the relation for de Broglie wavelength as:

Substituting equation (2) in equation (1), we get the relation:

Hence, the kinetic energy of the electron is.

(B) Using equation (3), we can write the relation for the kinetic energy of the neutron as:

Hence, the kinetic energy of the neutron is or.