Question

Define threshold frequency.

Answer 1

Hint: In photoelectric effect, electrons are ejected due to the energy of beam incident which contains particles called photons, which hold a specific amount of energy. They transfer this energy to the electron on the metal surface, through collisions. But all frequencies of photons do not generate photoelectrons. The threshold frequency, as the name suggests is the threshold value or limit value of frequency needed for the electron to be ejected.

Formula used:
$E = h{f_ \circ } - K.E{._{\max }}$

Complete answer:

Initially, Newton devised the corpuscular theory of light, describing that light is made of divisible minute particles called corpuscles. This was rejected as it could not explain concepts like interference and diffraction.
Later, Max Planck proposed that light is actually made of tiny packets of energy called quanta or photons. Each of these packets is represented by $h\upsilon $. Here, h is Planck's constant and $\upsilon $ is the frequency.
Based on this idea, Albert Einstein formulated the photoelectric effect.
When a beam of light is incident on the surface of a metal, electrons are ejected. The beam is actually not a wave but made of these tiny packets of energy (photons). The electrons ejected are known as photo electrons. The effect is called photoelectric effect. It is mathematically given by,
$\eqalign{
  & E = h{\upsilon _ \circ } + {\left( {K.E.} \right)_{\max }} \cr
  & \cr} $
Where
$E$ is the energy of the incident beam
$h$ is the Planck’s constant
${\upsilon _ \circ }$ is the threshold frequency
${\left( {K.E.} \right)_{\max }}$ is the maximum kinetic energy.
Einstein found that electrons were ejected only when the frequency of the beam was more than a certain quantity for the electrons to be ejected. This frequency is called threshold frequency (${\upsilon _ \circ }$).

It is the minimum frequency required for the electrons to be ejected from the surface of the metal.
The minimum energy due the threshold frequency is called work function or threshold energy. It is given by $W = h{\upsilon _ \circ }$.

Note:
Photoelectric effect permitted for the explanation of particle nature of light, leading to wave-particle duality.
The ${\left( {K.E.} \right)_{\max }}$ is the kinetic energy experienced by the electron once it is ejected from the surface.
You have to understand that the threshold frequency will only eject the electron. Once it is ejected the ${\left( {K.E.} \right)_{\max }}$ will provide the necessary energy for the movement of electrons.
You have to keep in mind that every frequency of a photon does not lead to ejection of electrons due to this threshold frequency. The photon must have frequency greater the threshold frequency to generate photoelectrons.