Question 345: Dual Nature of Matter and Radiation

Question

A light of wavelength '$$\lambda$$' and intensity '$$\mathrm{I}$$' falls on photosensitive material. If '$$\mathrm{N}$$' photo electrons are emitted, each with kinetic energy 'E', then

Accepted Answer

To understand the relationship between kinetic energy (E) of photoelectrons, wavelength ($$\lambda$$) of incident light, and intensity ($$\mathrm{I}$$) of the light in the context of the photoelectric effect, we need to review the basics of the photoelectric effect. The photoelectric effect is governed by Einstein's equation:
$$E_{	ext{photon}} = h
u = h\frac{c}{\lambda}$$
where $$h$$ is Planck's constant, $$
u$$ is the frequency of the incident light, and $$c$$ is the speed of light.
According to the photoelectric effect:
$$E = E_{	ext{photon}} - \phi = h
u - \phi = h\frac{c}{\lambda} - \phi$$
Here, $$\phi$$ is the work function of the material.
From the above equation, it's clear that the kinetic energy $$E$$ of the emitted photoelectrons is inversely proportional to the wavelength $$\lambda$$ of the incident light and not dependent on the intensity ($$\mathrm{I}$$) of the light. Thus:
$$E \propto \frac{1}{\lambda}$$
Additionally, the number of photoelectrons ($$\mathrm{N}$$) emitted is directly proportional to the intensity of the incident light. This is because the intensity of the light corresponds to the number of photons hitting the surface per unit time. Therefore:
$$\mathrm{N} \propto \mathrm{I}$$
Combining these relationships, the correct option is:
Option D: $$\mathrm{E} \propto \frac{1}{\lambda}, \mathrm{N} \propto \mathrm{I}$$

Answer

$$\mathrm{E} \propto \mathrm{I}, \mathrm{N} \propto \lambda$$

Answer

$$\mathrm{E} \propto \mathrm{I}, \mathrm{N} \propto \mathrm{I}$$

Answer

$$\mathrm{E} \propto \mathrm{I}, \mathrm{N} \propto \frac{1}{\lambda}$$

Answer

$$\mathrm{E} \propto \frac{1}{\lambda}, \mathrm{N} \propto \mathrm{I}$$

Dual Nature of Matter and Radiation

A light of wavelength '$\lambda' and intensity '\mathrm{I}' falls on photosensitive material. If '\mathrm{N}$' photo electrons are emitted, each with kinetic energy 'E', then

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