When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have m

step 1 Hello everyone. In this question we will learn about some basic concepts of the photoelectric ef

When photon of energy 4.0 eV strikes the surface of a metal...

When photon of energy $4.0 \mathrm{eV}$ strikes the surface of a metal $A$, the ejected photoelectrons have maximum kinetic energy $T_{A} \mathrm{eV}$ and de-Broglie wavelength $\lambda_{A}$ The maximum kinetic energy of photoelectrons liberated from another metal $B$ by photon of energy $4.50 \mathrm{eV}$ is $T_{B}=\left(T_{A}-150\right) \mathrm{eV}$. If the de-Broglie wavelength of these photoelectrons $\lambda_{B}=2 \lambda_{A}$, then (a) the work function of $A$ is $1.50 \mathrm{eV}$ (b) the work function of $B$ is $4.0 \mathrm{eV}$ (c) $T_{A}=2.00 \mathrm{eV}$ (d) All of the above

When photon of energy $4.0 \mathrm{eV}$ strikes the surface of a metal $A$, the ejected photoelectrons have maximum kinetic energy $T_{A} \mathrm{eV}$ and de-Broglie wavelength $\lambda_{A}$ The maximum kinetic energy of photoelectrons liberated from another metal $B$ by photon of energy $4.50 \mathrm{eV}$ is $T_{B}=\left(T_{A}-150\right) \mathrm{eV}$. If the de-Broglie wavelength of these photoelectrons $\lambda_{B}=2 \lambda_{A}$, then
(a) the work function of $A$ is $1.50 \mathrm{eV}$
(b) the work function of $B$ is $4.0 \mathrm{eV}$
(c) $T_{A}=2.00 \mathrm{eV}$
(d) All of the above

Key Concepts

Photoelectric Effect

This is the phenomenon where electrons are emitted from a material when it is exposed to electromagnetic radiation of sufficient energy. The process is described by comparing the energy of the incoming photons with the work function of the material, determining whether electrons will be ejected and with what kinetic energy.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a metal. It serves as a threshold in the photoelectric effect; any photon with energy below this value will not eject electrons, while excess energy beyond the work function appears as the kinetic energy of the emitted electron.

Photoelectron Kinetic Energy

This is the maximum kinetic energy that the photoelectrons can have when they are ejected from the surface. It is given by subtracting the work function from the energy of the incident photons. This concept is central to the quantitative analysis of the photoelectric effect and helps relate the observed energies to the intrinsic properties of the metal.

de Broglie Wavelength

In quantum mechanics, the de Broglie wavelength relates to the wave-like behavior of particles, including electrons. It is derived from the momentum of the particle and reflects the fact that even particles with mass can exhibit wave characteristics. In the context of the photoelectric effect, the de Broglie wavelength of an emitted electron is dependent on its kinetic energy.

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