Question

The work function of sodium is 2.75eV. What will be the kinetic energy of the emitted electron when a proton of energy 3.54eV is incident on the surface of sodium.

Answer 1

Hint: Here we use the relation that the work function of a material is dependent on the kinetic energy and the incident radiation energy. Further, we use the given values and find the kinetic energy on the surface of sodium. Sodium is a metal, it has atomic number 11.

Formula used:
$h_f=K.E+\varphi$

Complete step-by-step answer:
Work function is the property of a material. It is defined as the minimum quantity of energy which is required to remove an electron to infinity from the surface of the material.
Kinetic energy of an object is the energy that it possesses due to motion of the object. It can be defined as the work needed to accelerate a body or object of given mass from rest to its velocity. When an object gains this energy during its acceleration, the object maintains this kinetic energy unless its speed or velocity changes.
Given:

$\begin{array}{rl}& \varphi =2.75eV\\ & h_f=3.54eV\end{array}$

We know,

$\begin{array}{rl}& h_f=K.E+\varphi \\ & 3.54=K.E+2.75\\ & K.E=3.54-2.75\\ & \Rightarrow K.E=0.79eV\end{array}$

Therefore, the kinetic energy of sodium having a work function is 2.75eV, when a proton of energy 3.54eV is incident on the surface of sodium is 0.79 eV.

Additional Information: Sodium is a chemical element with symbol Na. it has atomic number 11. It is a soft, silvery-white, highly reactive metal. In the periodic table, sodium comes under group 1. Melting point of sodium is 97.79°C.
When electrons are emitted when electromagnetic radiation, such as light, hits the material or its surface is called the photoelectric effect. The work function for photoelectric effect is different for different materials. It depends upon the intensity of light.

Note: Total energy is given by the sum of potential energy and kinetic energy. Work function of a material is dependent on its kinetic energy. The unit of energy here is electron volts which is $1.602\times {10}^{-19}Joule$. The S.I unit of energy is Joule.