Which metal will be suitable for a photo electric cell using light of wavelength 4000 Å. The work functions of sodium and copper are respectively 2.0 eV and 4.0 eV.

Options

A. sodium
B. copper
C. Both
D. None of both

Answer

To determine which metal is suitable for a photoelectric cell using light of wavelength 4000 Å, we need to compare the incident energy of the light with the work functions of sodium and copper.

### Step-by-step Solution:

1. **Identify the Wavelength and Work Functions**:
- Given wavelength (λ) = 4000 Å (1 Å = 10^-10 m)
- Work function of sodium (Φ_Na) = 2.0 eV
- Work function of copper (Φ_Cu) = 4.0 eV

2. **Convert Wavelength to Energy**:
- Use the formula for energy (E) of a photon:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) (Planck's constant) = 4.1357 × 10^-15 eV·s
- \( c \) (speed of light) = 3 × 10^8 m/s
- Convert λ from Ångstroms to meters: \( λ = 4000 \, \text{Å} = 4000 \times 10^{-10} \, \text{m} = 4 \times 10^{-7} \, \text{m} \)

3. **Calculate the Energy**:
- Substituting the values into the energy formula:
\[ E = \frac{(4.1357 \times 10^{-15} \, \text{eV·s})(3 \times 10^8 \, \text{m/s})}{4 \times 10^{-7} \, \text{m}} \]
- Performing the calculation:
\[ E = \frac{1.24071 \times 10^{-6} \, \text{eV·m}}{4 \times 10^{-7} \, \text{m}} = 3.101775 \, \text{eV} \approx 3.1 \, \text{eV} \]

4. **Compare Incident Energy with Work Functions**:
- For sodium:
- Incident energy (3.1 eV) > Work function (2.0 eV)
- For copper:
- Incident energy (3.1 eV) < Work function (4.0 eV)

5. **Conclusion**:
- Since the incident energy is greater than the work function for sodium, sodium will emit electrons and thus is suitable for a photoelectric cell. Copper, on the other hand, will not emit electrons because the incident energy is less than its work function.

### Final Answer:
**Sodium is the suitable metal for a photoelectric cell using light of wavelength 4000 Å.**