JEE Physics 2025 Question with Solution

Given: Work function of Cs is $1.9 \, \text{eV}$, work function of Li is $2.5 \, \text{eV}$, and incident wavelength is $550 \, \text{nm}$.

Find: For which metal the photoelectric effect is possible.

For photoelectric emission to occur, the incident photon energy must be greater than the work function.

The energy of the incident photon is

$$E = \frac{1240}{\lambda} = \frac{1240}{550} \approx 2.25 \, \text{eV}$$

Now compare this with the work functions:

For Cs,

$$2.25 \, \text{eV} > 1.9 \, \text{eV}$$

So, photoelectric effect is possible for Cs.

For Li,

$$2.25 \, \text{eV} < 2.5 \, \text{eV}$$

So, photoelectric effect is not possible for Li.

Therefore, the correct option is B.

Given:

• $h = 6.626 \times 10^{-34} \, \text{J s}$
• $c = 3 \times 10^8 \, \text{m/s}$
• $\lambda = 550 \times 10^{-9} \, \text{m}$
• $\phi_{Cs} = 1.9 \, \text{eV}$
• $\phi_{Li} = 2.5 \, \text{eV}$

Find: Which metal shows photoelectric emission.

Photon energy is given by

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

Substituting the values,

$$E = \frac{6.626\times10^{-34}\times3\times10^8}{550\times10^{-9}} = 3.613\times10^{-19} \, \text{J}$$

Convert this into electron volt using

$$1 \, \text{eV} = 1.602\times10^{-19} \, \text{J}$$

So,

$$E = \frac{3.613\times10^{-19}}{1.602\times10^{-19}} = 2.26 \, \text{eV}$$

Now compare:

• For Cs, $2.26 \, \text{eV} > 1.9 \, \text{eV}$, so photoelectric effect occurs.
• For Li, $2.26 \, \text{eV} < 2.5 \, \text{eV}$, so photoelectric effect does not occur.

Therefore, only Cs emits photoelectrons. The correct option is B.