Question

Light of frequency \[\upsilon \] is incident on a substance of threshold frequency \[{\upsilon _0}({\upsilon _0} < \upsilon )\]. The energy of the emitted photoelectron will be:
A.\[h(\upsilon - {\upsilon _0})\]
B. \[\dfrac{h}{\upsilon }\]
C. \[he(\upsilon - {\upsilon _0})\]
D. \[\dfrac{h}{{{\upsilon _0}}}\]

Answer 1

Hint: A light with energy \[h\upsilon \] is incident on a photosensitive surface and causes photoelectric emission. If the frequency of incident radiation is greater than the threshold frequency then photoemission will occur.

Formula used:
Work function is given as:
\[\phi = h{\upsilon _0}\]
Where h is Planck's constant and \[{\upsilon _0}\] is the threshold frequency.

Complete step by step solution:
Einstein gives the phenomenon of the photoelectric effect on the basis of Plank’s theory. In the photoelectric effect, the kinetic energy of photo-electrons emitted from the metal surface E and \[\phi \] is the work function of the metal. Thus the total energy of a photon is equal to the sum of the energy utilized to eject an electron and the maximum kinetic energy of electrons. As we know the maximum kinetic energy of photoelectrons is,
\[K{E_{\max }} = E - \phi {\rm{ }}\]
\[\Rightarrow K{E_{\max }} = h\upsilon - \phi {\rm{ }}\]

Given frequency of light is \[\upsilon \]. Threshold frequency of light \[{\upsilon _0}\]. For a given metal, if the threshold frequency of light is \[{\upsilon _0}\] then an amount of energy \[\phi \]of the photon of light will be spent in ejecting the electron out of the metal. The work function \[\phi \] is defined as the minimum amount of energy required to induce photoemission of electrons from a metal surface and is given as
\[\phi = h{\upsilon _0}\]
Now using this above, we have
\[K{E_{\max }} = h\upsilon - h{\upsilon _0}\]
\[\therefore KE = h(\upsilon - {\upsilon _0})\]
Therefore, the energy of the emitted photoelectron will be \[h(\upsilon - {\upsilon _0})\].

Hence option A is the correct answer.

Note: The photoelectric effect happens when sufficiently frequent light is impacted on a metal surface, causing electrons to be expelled from it. According to Einstein, each light particle possesses energy known as a photon and behaves like a particle. The photon energy is transmitted to the electron when it strikes the metal surface.