Class 12 Physics

Few problems and their solutions from this chapter are given below:

Question:

Consider a beam of electrons (each electron with energy E₀) incident on a metal surface kept in an evacuated chamber. Then,

(a) No electrons will be emitted as only photons can emit electrons

(b) Electrons can be emitted but all with an energy, E₀

(c) Electrons can be emitted with any energy, with a maximum of E₀ − Φ (Φ is the work function)

(d) Electrons can be emitted with any energy, with a maximum of E₀

Solution:(d)

When a beam of electrons of energy E₀ is incident on a metal surface kept in an evacuated chamber due to elastic collision electrons can be emitted with maximum energy E₀. When part of incident energy of electron is used in liberating the electrons from the surface of metal, then electrons can be emitted with energy less than E₀.

Question:

A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de-Broglie wavelength of the particle varies cyclically between two values λ₁ λ₂ with λ₁ > λ₂. Which of the following statement are true?

(a) The particle could be moving in a circular orbit with origin as centre

(b) The particle could be moving in an elliptic orbit with origin as its focus

(c) When the de-Broglie wavelength is λ₁ the particle is nearer the origin than when its value is λ₂

(d) When the de-Broglie wavelength is λ₂, the particle is nearer the origin than when its value is λ₁

Solution: (b, d)

If particle is moving in an elliptical orbit with origin as its one focus, then the de-Broglie wavelength of the particle can be varying cyclically between two values λ₁ and λ₂.

Let the speed of particle at A and B be v₁ and v₂ respectively and origin is at focus O.

Also, let us suppose λ₁ and λ₂ are the de-Broglie wavelengths associated with particle while moving at A and B respectively. Then,

We are given that, λ₁ > λ₂

Using (3), we get

 v₁ > v₂

According to law of conservation of angular momentum, the particle moves faster when it is closer to focus. From the figure given above, we note that origin O is closed to P than A.

Question:

There are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. Can there be stable substances which absorb photons of larger wavelength and emit light of shorter wavelength.

Solution:

If the materials absorb photons of shorter wavelength, then the energy of the incident photon on the material is high and the energy of emitted photon is low when it has a longer wavelength.

But, the energy of the incident photon is low for the substances which have to absorb photons of larger wavelength. Similarly, the energy of emitted photon is high to emit light of shorter wavelength. So, according to this statement material has to supply the energy for the emission of photons.

For a stable substance, it can’t be possible.

Question:

Do all the electrons that absorb a photon come out as photoelectrons?

Solution:

In photoelectric effect, most of the electrons get scattered into the metal by absorbing a photon. Therefore, all the electrons that absorb a photon don’t come out as photoelectron.

Question:

Consider figure for photoemission. How would you reconcile with momentum-conservation? Note light (photons) have momentum in a different direction than the emitted electrons.

Solution:

The momentum of incident photon is transferred to the metal during the photoelectric emission. The atoms of a metal absorb the photon and its momentum is transferred mainly to the nucleus and electrons. The excited electron is emitted.

Therefore, the conservation of momentum is to be considered as the momentum of incident photon transferred to the nucleus and electrons.