Ncert Exercises & Solutions

(i) In the explanation of the photoelectric effect, we assume one photon of frequency $ν$ collides with an electron and transfers its energy. This leads to the equation for the maximum energy $E_{\max}$ of the emitted electron as

$E_{\max} = hν - ϕ_{0}$
where $ϕ_{0}$ is the work function of the metal. If an electron absorbs 2 photons (each of frequency $ν$ ), what will be the maximum energy for the emitted electron?

(ii) Why is this fact (two-photon absorption) not taken into consideration in our discussion of the stopping potential?

Hint: The energy absorbed by the electron will be equal to the energy of two photons.

Step 1: Find the final energy of the emitted electron.

(i) Here it is given that, an electron absorbs 2 photons each of frequency

ν

, then,

ν

’=2

ν

where,

ν

’ is the frequency of emitted electron.
Given,

E_{\max} = hν - ϕ_{0}

Now, the maximum energy for emitted electrons is:

E_{\max} = h (2 ν) - ϕ_{0} = 2 hν - ϕ_{0}

(ii) The probability of absorbing 2 photons by the same electron is very low. Hence, such emission will be negligible.

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