If the two metals `A` and `B` are exposed to radiation of wavelength `350nm`.The work functions of metals `A` and `B` are `4.8eV` and `2.2eV` .Then choose the correct option.

Options

A. Both metals `A` and `B` will emit photo-electrons
B. Metal B will not emit photo-electrons
C. Both metals `A` and `B` will not emit photo-electrons
D. Metal A will not emit photo-electrons

Answer

To solve the problem, we need to determine whether each metal (A and B) can emit photoelectrons when exposed to radiation of wavelength 350 nm. We will use the concept of photoelectric effect, which states that a photon can eject an electron from a metal if its energy is greater than the work function of that metal.

### Step-by-Step Solution:

1. **Calculate the Energy of the Incident Photon:**
The energy \( E \) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) (Planck's constant) = \( 4.1357 \times 10^{-15} \) eV·s
- \( c \) (speed of light) = \( 3 \times 10^8 \) m/s
- \( \lambda \) (wavelength) = \( 350 \) nm = \( 350 \times 10^{-9} \) m

Substituting the values:
\[ E = \frac{(4.1357 \times 10^{-15} \text{ eV·s})(3 \times 10^8 \text{ m/s})}{350 \times 10^{-9} \text{ m}} \]

2. **Perform the Calculation:**
\[ E = \frac{(4.1357 \times 3)}{350} \times 10^{-15 + 8 + 9} \]
\[ E = \frac{12.4071}{350} \times 10^{-15 + 17} \]
\[ E = \frac{12.4071}{350} \times 10^{-7} \text{ eV} \]
\[ E \approx 0.0354 \times 10^{7} \text{ eV} = 3.54 \text{ eV} \]

3. **Compare the Energy of the Photon with the Work Functions:**
- Work function of metal A, \( \phi_A = 4.8 \) eV
- Work function of metal B, \( \phi_B = 2.2 \) eV

Now we compare:
- For metal A:
\[ E < \phi_A \quad (3.54 \text{ eV} < 4.8 \text{ eV}) \]
This means metal A will **not** emit photoelectrons.

- For metal B:
\[ E > \phi_B \quad (3.54 \text{ eV} > 2.2 \text{ eV}) \]
This means metal B **will** emit photoelectrons.

4. **Conclusion:**
Based on the comparisons, we conclude that:
- Metal A will not emit photoelectrons.
- Metal B will emit photoelectrons.

Thus, the correct option is that only metal B will emit photoelectrons.