Threshold frequency of a metal is f0 . When light of...

Threshold frequency of a metal is $f_{0} .$ When light of frequency $v=2 f_{0}$ is incident on the metal plate, maximum velocity of $e^{-}$ emitted is $v_{1}$. When frequency of incident radiation is $5 f_{0}$, maximum velocity of emitted $e^{-}$ is $v_{2}$. Find ratio of $\frac{v_{1}}{2}$ : (a) $1: 4$ (b) $1: 2$ (c) $2: 1$ (d) none of these

Threshold frequency of a metal is $f_{0} .$ When light of frequency $v=2 f_{0}$ is incident on the metal plate, maximum velocity of $e^{-}$ emitted is $v_{1}$. When frequency of incident radiation is $5 f_{0}$, maximum velocity of emitted $e^{-}$ is $v_{2}$. Find ratio of $\frac{v_{1}}{2}$ :
(a) $1: 4$
(b) $1: 2$
(c) $2: 1$
(d) none of these

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Key Concepts

Kinetic Energy and Velocity Relationship

In the photoelectric effect, the excess energy of the photon beyond the work function becomes the kinetic energy of the emitted electron. This is represented by the equation ½ mv² = h(f - f?), where m is the electron mass and v is its velocity. Since velocity is related to the square root of the kinetic energy, changes in the frequency of the incident light lead to changes in the electron's speed according to this square-root dependence.

Work Function and Threshold Frequency

The work function is the minimum energy required to eject an electron from the surface of a material. The threshold frequency (f?) is defined as the minimum frequency of light needed for electron emission; mathematically, it corresponds to the energy h·f? equal to the work function. Any photon with frequency lower than this will not lead to electron emission.

Photoelectric Effect

This is the phenomenon in which electrons are emitted from a material (usually a metal) when light of sufficient frequency shines on it. The key relation is that the energy of the incident photon (given by E = hf, where h is Planck's constant and f is the frequency) must exceed the work function of the material, which is related to the threshold frequency.

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