Question

With reference to photoelectric effect, define threshold wavelength.

Answer 1

Hint: Threshold frequency is the minimum frequency of the light to remove the electrons for a metal. Use the relation between the frequency and wavelength of light i.e. $\nu ={\displaystyle \frac{c}{\lambda }}$ to understand the meaning of threshold wavelength.

Formula used:
$\nu ={\displaystyle \frac{c}{\lambda }}$

Complete step-by-step answer:
Let us first understand what photo electric effect is. The photoelectric theory was given by Albert Einstein. According to this theory, when light falls on a metal, the metal emits electrons.
Light is considered to be made of small energy packages. These energy packages are massless particles called photons. Photons travel with speed equal to the speed of light. A photon possesses an energy equal to $E=h\nu$, h is the Planck’s constant and $\nu$ is the frequency of the light.
When a photon falls on a metal, it collides with an electron. Due to this, the electron absorbs the energy of the photon. If the energy is enough to break the interatomic forces of attraction, then the electron will be free from the metal.
The minimum energy required to make an electron free from the interatomic forces is called work function ($\varphi$).
Therefore, if we want to just remove an electron from a metal, the energy of the photon must be equal to the work function. The frequency of the light for which its energy is equal to the work function is called threshold frequency ${\nu }_0$.
Therefore, $\varphi =h{\nu }_0$.
Let us use the relation between the frequency and the wavelength of light, i.e. $\nu ={\displaystyle \frac{c}{\lambda }}$.
When the light wave has threshold frequency, its wavelength is called threshold wavelength (${\lambda }_0$).
Hence, ${\nu }_0={\displaystyle \frac{c}{{\lambda }_0}}$
Threshold frequency is the minimum frequency of the light required to remove an electron out of a metal. Since wavelength of light is inversely proportional to its frequency, the threshold wavelength is the maximum wavelength of the light for which the metal will emit electrons.

Note: Remember the difference between the threshold frequency and the threshold wavelength.
The metal will emit electrons only if the frequency of the light incident on the metal is more than the threshold frequency. However, if the wavelength is more than the threshold wavelength, then the metal will not emit electrons.