Question

If the frequency of incident light falling on a photosensitive metal is doubled, the kinetic energy of the emitted photoelectron

A.)unchanged
B.halved
C.)doubled
D.)more than twice its initial value
E.)reduced to $\dfrac{1}{4}th$

Answer 1

Hint – Start the question by describing what photoelectric effect is and what is its significance. Then move on to calculate the kinetic energy of both the conditions by using Einstein’s photoelectric equation$(KE = hv - \phi )$ and compare them.

Complete step by step answer:
After the concept of photon came out, energy of a photon could be calculated by using Planck’s equation,

${E_{photon}} = hv$

Where,

${E_{photon}} =$Energy of photons in joules$(J)$,
$h =$Planck’s constant$(6.626 \times {10^{ - 34}}Js$,
And $v =$frequency of light in $Hz$

Let’s assume $KE$is the initial kinetic energy of the photoelectron, $KE'$ be the kinetic energy after increasing the frequency, and $v$ be the initial frequency. So the final frequency becomes$2v$.

By Einstein’s photoelectric equation

$KE = hv - \phi$

By Einstein’s photoelectric equation, the initial kinetic energy of photoelectrons is

$KE = hv - \phi$

$\Rightarrow hv = KE + \phi$(Equation 1)

Kinetic Energy after the increase in frequency is

$KE' = 2hv - \phi$

Substituting the value of $hv$from equation 1

$\Rightarrow KE' = 2(KE + \phi ) - \phi$
$\Rightarrow KE' = 2KE + 2\phi - \phi$
$\Rightarrow KE' = 2KE + \phi$

Hence, the Kinetic energy increases by more than double, option C is the correct choice.

Additional Information: The problem is referring to a phenomenon called the photoelectric effect. Photoelectric effect basically means the discharge of an electron (in this case called a photoelectron) from the surface of a metal plate, when it is hit by an electromagnetic wave (referred to as incident light in the problem).
This effect can be called a major contributor to the acceptance of the dual nature of light. You see, in the 19th century scientists tried to explain this effect with the help of classical physics, where light was considered to have particle nature. But to solve the mystery of this effect scientists had to accept the wave nature of light and thus the concept of dual nature of light came to life.

Note– Although in the case of photoelectric effect the ejected electrons are called photoelectrons, but their behavior and properties are exactly like normal electrons. The prefix, photo- is used to describe that the electrons ejected, have done so, only by absorbing the energy of the incident light or electromagnetic radiation).