An ultraviolet light of wavelength 2000 Å irradiates a photo cell made of molybdenum metal . If the stopping potential is `-1.5`V , what is the work function of the metal ?

Options

A. `2.5 xx 10^(-19)` J
B. `5 xx 10^(-19)` J
C. `7.5 xx 10^(-19) J`
D. `1 xx 10^(-19)` J

Answer

To solve the problem, we need to find the work function (φ) of molybdenum when ultraviolet light of wavelength 2000 Å is incident on it, and the stopping potential is -1.5 V.

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Wavelength (λ) = 2000 Å = 2000 × 10^(-10) m
- Stopping potential (V) = -1.5 V

2. **Convert the Wavelength to Meters:**
\[ \lambda = 2000 \, \text{Å} = 2000 \times 10^{-10} \, \text{m} = 2 \times 10^{-7} \, \text{m} \]

3. **Use the Stopping Potential Formula:**
The stopping potential (V) is related to the energy of the incident photons and the work function (φ) of the metal by the equation:
\[ eV = h\nu - φ \]
where:
- \( e \) is the elementary charge (\( 1.6 \times 10^{-19} \, \text{C} \))
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \))
- \( \nu \) is the frequency of the incident light.

4. **Calculate the Frequency (ν):**
The frequency can be calculated using the relation:
\[ \nu = \frac{c}{\lambda} \]
where \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)).
\[ \nu = \frac{3 \times 10^8}{2 \times 10^{-7}} = 1.5 \times 10^{15} \, \text{Hz} \]

5. **Calculate the Energy of the Photons (hν):**
\[ h\nu = h \times \nu = 6.626 \times 10^{-34} \times 1.5 \times 10^{15} \]
\[ h\nu = 9.939 \times 10^{-19} \, \text{J} \]

6. **Substitute Values into the Stopping Potential Equation:**
Rearranging the stopping potential equation gives:
\[ φ = h\nu - eV \]
Substitute the values:
\[ φ = 9.939 \times 10^{-19} - (1.6 \times 10^{-19} \times -1.5) \]
\[ φ = 9.939 \times 10^{-19} + 2.4 \times 10^{-19} \]
\[ φ = 12.339 \times 10^{-19} \, \text{J} \]

7. **Convert the Work Function to Electron Volts (eV):**
To convert joules to electron volts, divide by the charge of an electron:
\[ φ = \frac{12.339 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 7.71 \, \text{eV} \]

### Final Answer:
The work function of molybdenum is approximately **7.71 eV**.