Question

The work function of zinc is 3.74eV. If the sphere of zinc is illuminated by the X-rays of wavelength 12Å. Find the maximum potential production on the sphere, h = 6.625 $\times 10^{-34}$ Js.

Answer 1

Hint: The work function of a material is dependent on the kinetic energy and the incident radiation energy. Zinc is a metal of atomic number 30. When the potential energy is maximum the kinetic energy and speed is zero.

Formula used:
$\eqalign{
  & Energy = Ev = (hc/\lambda ) - \phi \cr
  & \because V = 1/e[(hc/\lambda ) - \phi ] \cr} $

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.
Given:
$ \phi = 3.74eV = 3.74 \times 1.6 \times {10^{ - 19}}J $
 $ \lambda = 12{A^ \circ } = 12 \times {10^{ - 10}}m $
We know that,
$ Energy = eV = (hc/\lambda ) - \phi $
$ \because V = 1/e[(hc/\lambda ) - \phi ] $
$ V = (hc/e\lambda ) - (\phi /e) $
$ V = [\{ 6.62 \times {10^{ - 34}} \times 3 \times {10^8}\} /\{ 1.6 \times {10^{ - 19}} \times 12 \times {10^{ - 10 \to }}\} ] - 3.74 $
$ \Rightarrow V = 1.031 \times {10^3} - 3.74 $
$ \therefore {V_{\max }} = 1031Volts $
Therefore, the maximum potential on the surface of the sphere when the work function of zinc is 3.74eV and if the sphere of zinc is illuminated by the x-rays of wavelength 12Å is 1031 V.

Additional Information: Zinc ia a chemical element with the symbol Zn and it has atomic number 30. Zinc is slightly brittle metal at room temperature. It has a blue-silvery appearance when oxidation is removed. It is the first element of the 12th group in periodic table and present in 4th period in periodic table. The melting point of zinc is 692.68K.
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. At the maximum height the potential energy is maximum and kinetic energy is zero.