Question

The maximum kinetic energy of photoelectrons coming out of a metal surface is \(10 \, \text{eV}\). The minimum voltage required to stop the emission of electrons from this metal surface is:

• A. \(10 \, V\)
• B. \(5 \, V\)
• C. \(-5 \, V\)
• D. \(-10 \, V\)

Hint:

Stopping potential is always negative because it opposes electron motion.

Answer 1

The Correct Option is D

To find the minimum voltage required to stop the emission of electrons from a metal surface, we need to apply the concept of stopping potential in the photoelectric effect.

The photoelectric effect describes the emission of electrons (photoelectrons) from a metal surface when it is illuminated by light of a certain frequency (or above a certain threshold frequency). The maximum kinetic energy (\(K_{\text{max}}\)) of these electrons can be expressed using the equation:

\(K_{\text{max}} = eV_{\text{stop}}\)

where:

• \(e\) is the charge of an electron (\(1.6 \times 10^{-19} \, \text{C}\)).
• \(V_{\text{stop}}\) is the stopping potential (voltage) required to stop the electrons.

Given, the maximum kinetic energy \(K_{\text{max}} = 10 \, \text{eV}\). To stop even the most energetic photoelectrons, the stopping potential must be equal to or greater than the kinetic energy of these photoelectrons.

By rearranging the formula, we have:

\(V_{\text{stop}} = \frac{K_{\text{max}}}{e} = 10 \, \text{V}.\)

Since the units are already matched (electron volts for both kinetic energy and potential), we see that \(V_{\text{stop}} = 10 \, \text{V}\) directly represents the stopping potential without further conversion. However, to stop electrons, this potential is in reverse to the potential applied usually, hence \(V_{\text{stop}} = -10 \, \text{V}\).

Thus, the minimum voltage required to stop the emission of electrons is:

\(-10 \, \text{V}\)