Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 14

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Energy of a photon

Energy of a Photon

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Q: 29. The work function for the following metals is given:

. Which of these metals will not give photoelectric emission for a radiation of wavelength 3300 from a laser placed away from the photocell? What happens if the laser is brought nearer and placed away?

Answer:

Mo and Ni will not show photoelectric emission is both cases

Wavelength for a radiation,

Speed of light,

Planck’s constant,

The energy of incident radiation is given as:

It can be observed that the energy of the incident radiation is greater than the work function of Na and K only. It is less for Mo and Ni. Hence, Mo and Ni will not show photoelectric emission.

If the source of light is brought near the photocells and placed away from them, then the intensity of radiation will increase. This does not affect the energy of the radiation. Hence, the result will be the same as before. However, the photoelectrons emitted from Na and K will increase in proportion to intensity.

Q: 30. Light of intensity falls on a sodium photo-cell of surface area. Assuming that the top layers of sodium absorb the incident energy, estimate time required for photoelectric emission in the wave-picture of radiation. The work function for the metal is given to be about. What is the implication of your answer?

Answer:

Intensity of incident light,

Surface area of a sodium photocell,

Incident power of the light,

Work function of the metal,

Number of layers of sodium that absorbs the incident energy,

We know that the effective atomic area of a sodium atom, is

Hence, the number of conduction electrons in layers is given as:

The incident power is uniformly absorbed by all the electrons continuously. Hence, the amount energy absorbed per second per electron is:

Time required for photoelectric emission:

The time required for the photoelectric emission is nearly half a year, which is not practical. Hence, the wave picture is in disagreement with the given experiment.

Q: 31. Crystal diffraction experiments can be performed using, or electrons accelerated through appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the wavelength of the probe equal to )

Mass of an electron,

Planck’s constant,

Charge on an electron,

The kinetic energy of the electron is given as:

Where,

Velocity of the electron

Momentum (p) of the electron

According to the de Broglie principle, the de Broglie wavelength is given as:

Energy of a photon,

Hence, a photon has a greater energy than an electron for the same wavelength.