Question

If threshold wavelength for sodium is 6800 \[\mathop A\limits^0 \] then the work function will be
A. \[1.8{\rm{ }}eV\]
B. \[{\rm{2}}{\rm{.5 }}eV\]
C. \[{\rm{2}}{\rm{.1 }}eV\]
D. \[{\rm{1}}{\rm{.4 }}eV\]

Answer 1

Hint: The work function is defined as the smallest amount of energy necessary to cause electron photoemission from a metal surface. The threshold wavelength is the greatest wavelength that incoming light must have in order for the photoelectric effect to occur. The threshold wavelength is determined by the material's work function.

Formula used:
Work function is given as:
\[\phi = h\upsilon = \dfrac{{hc}}{{{\lambda _0}}}\]
Where h is Planck’s constant, c is the speed of light, \[\upsilon \] is the frequency of incident light and \[{\lambda _0}\] is the threshold frequency.
1eV=\[1.6 \times {10^{ - 19}}J\]

Complete step by step solution:
The threshold wavelength for sodium is \[{\lambda _0} = \]6800 \[\mathop A\limits^0 \]. As we know that the work function is the minimum quantity of energy required to eject the electron from the metal surface. Work energy is given as,
\[\phi = \dfrac{{hc}}{{{\lambda _0}}} = \dfrac{{12375{\rm{\,eV}} \cdot \mathop A\limits^0 }}{{6800{\rm{ }}\mathop A\limits^0 }}\]
\[\therefore \phi = 1.8{\rm{\,eV}}\]
Therefore, the work function will be \[\phi = 1.8{\rm{\,eV}}\]

Hence option A is the correct answer.

Additional information: The photoelectric effect is the phenomenon in which when light arises on a metal surface then the electrons are ejected from it. These electrons released are known as photoelectrons. The threshold frequency is known as the minimum wavelength that the light should have for the photoelectric effect. So if the wavelength of the light is below the frequency of the threshold level, there will be no photoelectric effect. The threshold wavelength is commonly known as the threshold frequency. The minimum quantity of energy required to eject the electron from the metal surface is defined as the work function. The work function is different for different materials.

Note: Students frequently make errors while drafting the photoelectric effect equation given by Einstein. Always keep in mind that the incident radiation's energy is calculated as the sum of the photoelectron's kinetic energy and the metal's work function.