The threshold wavelength for emission of photoelectrons from a metal surface is `6xx10^(-7)` m. What is the work function of the material of the metal surface ?

Options

A. `6.66xx10^(-19)J`
B. `4.44xx10^(-19)J`
C. `3.33xx10^(-19)J`
D. `5.55xx10^(-19)J`

Answer

To find the work function of the material of the metal surface given the threshold wavelength, we can use the formula:

\[ \phi = \frac{hc}{\lambda} \]

where:
- \(\phi\) is the work function,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\)),
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the threshold wavelength (\(6 \times 10^{-7} \, \text{m}\)).

### Step-by-step Solution:

1. **Identify the given values**:
- Threshold wavelength, \(\lambda = 6 \times 10^{-7} \, \text{m}\)
- Planck's constant, \(h = 6.626 \times 10^{-34} \, \text{J s}\)
- Speed of light, \(c = 3 \times 10^8 \, \text{m/s}\)

2. **Substitute the values into the formula**:
\[ \phi = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{6 \times 10^{-7} \, \text{m}} \]

3. **Calculate the numerator**:
\[ hc = 6.626 \times 10^{-34} \times 3 \times 10^8 = 1.9878 \times 10^{-25} \, \text{J m} \]

4. **Calculate the work function**:
\[ \phi = \frac{1.9878 \times 10^{-25} \, \text{J m}}{6 \times 10^{-7} \, \text{m}} = 3.312 \times 10^{-19} \, \text{J} \]

5. **Final result**:
The work function of the material of the metal surface is approximately:
\[ \phi \approx 3.312 \times 10^{-19} \, \text{J} \]