Question

: In the equation, $\text{hv = h}{{\text{v}}_{\text{0}}}\text{ + }\dfrac{\text{1}}{\text{2}}{{\text{m}}_{\text{e}}}{{\text{v}}^{\text{2}}}$, ${{\text{v}}_{\text{0}}}$is called:
A.Work function
B.Velocity of the ejected electron
C.Threshold frequency
D.Frequency of photon

Answer 1

The equation given here is Einstein's equation of photoelectric emission. This equation is based on the principle that light consists of small packets of energy that are called “quantum” or packets of energy.

Complete answer:
Einstein's equation of photoelectric emission is based on the emission of electrons from the surface of metals by the application of light energy. It has been observed that,
There is a minimum or cut-off or threshold frequency,${{\text{v}}_{\text{0}}}$, specific to the metal surface below which no emission of electrons can take place, no matter whatever be the intensity of the incident radiation or for how long it falls on the surface.
The maximum kinetic energy of the emerging electrons is independent of the intensity of the incident radiation but depends linearly on the frequency of the incident radiation.
Electrons start to eject immediately after the radiation shines on the surface of the metal surface without any detectable time delay.
For a given frequency of incident radiation, above ${{\text{v}}_{\text{0}}}$, the number of electrons emitted per unit time is proportional to the intensity of the incident radiation.
Hence, it is clear that ${{\text{v}}_{\text{0}}}$ is called the Threshold frequency.

Hence, the correct answer is option C.

Note:
In the year 1905, Einstein proposed individual quanta for electromagnetic radiation itself which later came to be known as the photon each carrying energy that is equal to $\text{hv}$, where “h” is called the Planck's constant whose value is equal to $\text{6}\text{.624 }\times\text{ 1}{{\text{0}}^{\text{-34}}}\text{J-sec}$.