# Threshold frequency,  is the minimum frequency which a photon must possess to eject an electron from a metal. It is different for different metals. When a photon of frequency $1.0\times 10^{15}\; s^{-1}$ was allowed to hit a metal surface, an electron having  of kinetic energy was emitted. Calculate the threshold frequency of this metal. Show that an electron will not be emitted if a photon with a wavelength equal to 600 nm hits the metal surface.

As per the quantum theory,

Therefore,

Where h represents the plank's constant, i.e.

As per the information provided in the question, we must calculate  which represents the threshold frequency of photons.

v = frequency of incident photons. As per the information provided,

electrons kinetic energy =

Therefore,

(which is, in fact, the threshold frequency)

The relation between frequency and wavelength can be represented  by the equation,

, where λ represents the wavelength and c represents the speed of light, i.e.

Here, in this case of the threshold frequency

Thus, the photon's maximum wavelength can be represented as,

Now, we know that  which is certainly greater than the calculated value of the . Thus, the electron will not be emitted in case a photon which has a wavelength that is equal to 600 nm hits the surface of the metal.

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