Power required to produce the same saturation current on irradiating a metal plate

To find the power required to produce the same saturation current on irradiating a metal plate, we need to consider the quantum yield of the photoelectric effect for the two different wavelengths.

Quantum yield of photoelectric effect

The quantum yield of the photoelectric effect represents the efficiency of converting photons into photoelectrons. It is defined as the ratio of the number of emitted photoelectrons to the number of incident photons.

For the first wavelength (λ1), the quantum yield is given by η1, and for the second wavelength (λ2), the quantum yield is given by η2.

Relationship between power and saturation current

The saturation current is directly proportional to the number of photoelectrons emitted per unit time. The number of photoelectrons emitted depends on the number of incident photons and the quantum yield.

The power of a light beam is related to the number of incident photons per unit time. Therefore, we can establish the following relationship:

Power ∝ Number of incident photons per unit time

Equating the saturation currents

Since the saturation currents are the same for both wavelengths, the number of emitted photoelectrons per unit time must also be the same. This implies that the number of incident photons per unit time must be the same for both wavelengths.

Using the relationship above, we can write:

Power1 * η1 = Power2 * η2

where Power1 is the power of the light beam with wavelength λ1, and Power2 is the power of the light beam with wavelength λ2.

Calculating the power required

To find the power required to produce the same saturation current on irradiating a metal plate, we can rearrange the equation above to solve for Power2:

Power2 = (Power1 * η1) / η2

Substituting the given values of Power1, η1, and η2 into the equation will give us the required power.

It is important to note that the power required for the same saturation current depends not only on the wavelength of the light beam but also on the quantum yield of the photoelectric effect for that particular wavelength.