Question

In a photoelectric effect, the energy of the photon striking a metallic surface is $5.6 \times {10^{ - 19}}J$. The kinetic energy of the ejected electrons is $12.0 \times {10^{ - 20}}J$. The work function is:
A. $6.4 \times {10^{ - 19}}J$
B. $6.8 \times {10^{ - 19}}J$
C. $4.4 \times {10^{ - 19}}J$
D. $6.4 \times {10^{ - 20}}J$

Answer 1

Hint: We can calculate the work function by subtracting the energy of the photon to the kinetic energy of the ejected electrons. We can use the formula to work function,
$W = E - {\text{Kinetic energy}}$
Where,
W=Work function
E=Energy of the photon

Complete step by step answer:
Given data contains,
The value of Energy of the photon striking on a metallic surface is $5.6 \times {10^{ - 19}}J$.
The kinetic energy of the ejected electrons is $12.0 \times {10^{ - 20}}J$.
We can define a phenomenon where electrons are liberated from the surface of metal when the light of enough frequency is incident upon is known as photoelectric effect. The energy carried by each particle of light is called quanta or photon depends on the light’s frequency as expressed,
$E = h\nu $
Where,
E = Energy of light particle/photon
H = Planck’s constant. The value of Planck’s constant is $6.6261 \times {10^{ - 34}}Js$.
$\nu $ = Frequency of light
A portion of the energy is used to remove the electron from the atom of metal and the rest is given to the emitted electron as kinetic energy. Electrons discharged from below the surface of metal lose little kinetic energy during the collision. All the kinetic energy is carried by the electrons present on the surface provided by the photon and contains maximum kinetic energy.
Mathematically, we can write the expression of photon energy by adding the energy needed to remove an electron and maximum kinetic energy of the electron.
$E = W + KE$
We know that $E = h\nu $,
$h\nu = W + KE$
$KE = h\nu - W$
The energy needed to remove an electron is called a work function and is given by W.
We can substitute the values of E and kinetic energy by rearranging the equation of Energy.
$h\nu = W + KE$
$\Rightarrow$ $W = E - KE$
$\Rightarrow$ $W = 5.6 \times {10^{ - 19}}J - 12.0 \times {10^{ - 20}}J$
$\Rightarrow$ $W = 4.4 \times {10^{ - 19}}J$
The work function is $4.4 \times {10^{ - 19}}\,J$.

So, the correct answer is Option C.

Note:
We also remember when exposed to electromagnetic radiation, a rise in the electrical conductivity of a nonmetallic solid is called photoconductivity. The rise in conductivity is because of the addition of free electrons released by collision with photons.