JEE Chemistry 2023 Question with Solution

Given: Light of wavelength $400 \, \text{nm}$ falls on the metals.

Find: The number of metals that will show the photoelectric effect.

The correct answer is $3$.

The photoelectric effect requires a photon with energy greater than the work function of the metal. A photon's energy is provided by

$$E=\frac{hc}{\lambda}$$

Where, $h$ = Planck's constant, $c$ = Velocity of light, $\lambda$ = Wavelength

here given $\lambda = 400 \, \text{nm}$

Then

$$E = \frac{6.6\times10^{-34}\times3\times10^8}{400\times 10^{-9}}$$

E in $\text{eV}$

$$E = \frac{6.6\times10^{-34}\times3\times10^8}{400\times 10^{-9}\times1.6\times10^{-19}}$$ $$E = 3 \, \text{eV}$$

The metals Li, Na, K and Mg have a work function less than the energy of a photon. In the presence of light with a wavelength of $400 \, \text{nm}$, they exhibit a photoelectric effect.

The solution states four metals satisfy the condition, but the extracted answer shown is $3$. Therefore, based on the provided source, the recorded answer is $3$.