Photoelectric emission is observed from a metal surface for...

Photoelectric emission is observed from a metal surface for frequencies $v_{1}$ and $v_{2}$ of the incident radiation $\left(v_{1}>v_{2}\right)$. If maximum kinetic energies of the photoelectrons in the two cases are in the ratio $1: K$, then the threshold frequency for the metal is given by (a) $\frac{v_{2}-v_{1}}{K-1}$ (b) $\frac{K v_{2}-v_{1}}{K-1}$ (c) $\frac{K v_{1}-v_{2}}{K}$ (d) $\frac{K v_{1}-v_{2}}{K-1}$

Photoelectric emission is observed from a metal surface for frequencies $v_{1}$ and $v_{2}$ of the incident radiation $\left(v_{1}>v_{2}\right)$. If maximum kinetic energies of the photoelectrons in the two cases are in the ratio $1: K$, then the threshold frequency for the metal is given by
(a) $\frac{v_{2}-v_{1}}{K-1}$
(b) $\frac{K v_{2}-v_{1}}{K-1}$
(c) $\frac{K v_{1}-v_{2}}{K}$
(d) $\frac{K v_{1}-v_{2}}{K-1}$

Key Concepts

Kinetic Energy of Emitted Electrons

In the context of the photoelectric effect, the kinetic energy of the emitted electrons is determined by the energy of the incident photon minus the work function of the material. This relationship is typically expressed by the equation K_max = h(v - v_0), where K_max is the maximum kinetic energy of the electrons, h is Planck’s constant, v is the frequency of the incident radiation, and v_0 is the threshold frequency. This concept is crucial for understanding how varying the frequency of light affects the energy of the emitted electrons.

Photoelectric Effect

The photoelectric effect refers to the phenomenon in which electrons are emitted from a material (typically a metal) when it is exposed to electromagnetic radiation of sufficiently high frequency. This effect was pivotal in the development of quantum mechanics as it demonstrated that light must have both wave and particle characteristics, and that energy is quantized.

Threshold Frequency

The threshold frequency is the minimum frequency of incident radiation required to eject electrons from the surface of a material. It is directly related to the material's work function, which is the minimum energy needed to overcome the attractive forces holding the electrons in the material. Only photons with energy equal to or greater than this threshold can cause photoemission.

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