Question

Work function of metal is \(4.2 \mathrm{eV}\) If ultraviolet radiation (photon) having energy \(6.2 \mathrm{eV}\), stopping potential will be........ (A) \(2 \mathrm{eV}\) (B) \(2 \mathrm{~V}\) (C) 0 (d) \(10.4 \mathrm{~V}\)

Short answer

The stopping potential for a metal with a work function of \(4.2 \mathrm{eV}\) when ultraviolet radiation of \(6.2 \mathrm{eV}\) is incident on it is (B) \(2 \mathrm{~V}\).

Step-by-step solution

List the given information

The given information is: Work function (W) = \(4.2\mathrm{eV}\) Photon energy (E) = \(6.2\mathrm{eV}\)

Calculate the energy difference

The energy difference (E - W) is the energy provided by the photon that is not used to overcome the work function. This energy is given by: E - W = \(6.2\mathrm{eV} - 4.2\mathrm{eV} = 2\mathrm{eV}\)

Convert eV to Joules

Since we will need to convert the energy difference into voltage, we first need to convert the energy from electron volts (eV) to Joules (J). The conversion factor is: \(1\mathrm{eV} = 1.6 \times 10^{-19} \mathrm{J}\) Therefore, the energy difference in Joules is: \(2\mathrm{eV} \times 1.6 \times 10^{-19}\frac{\mathrm{J}}{\mathrm{eV}} = 3.2 \times 10^{-19}\mathrm{J}\)

Calculate the stopping potential

Now, we can find the stopping potential using the formula: Stopping potential = (Photon energy - Work function) / Elementary charge Here, the elementary charge (q) is the charge of an electron, which is \(1.6 \times 10^{-19} \mathrm{C}\). Plugging in the values we have: Stopping potential = \(\frac{3.2 \times 10^{-19}\mathrm{J}}{1.6 \times 10^{-19} \mathrm{C}} = 2\mathrm{V}\)

Check the answer choices

The stopping potential we calculated is \(2\mathrm{V}\). Checking the answer choices, option (B) matches with our calculated value. Hence, the correct answer is: (B) \(2 \mathrm{~V}\)