The threshold wavelength for ejection of electrons from a metal is 230 nm. The work function for the photoelectric emission from the metal is

Options

A. 6.0×`10^(−19)`J
B. 8.6×`10^(−19)`J
C. 4.6×`10^(−19)`J
D. 6.0×`10^(−18)`J

Explanation

To find the work function for the photoelectric emission from the metal, we can use the relationship between the work function (W), Planck's constant (h), the speed of light (c), and the threshold wavelength (λ₀). The formula is given by:

\[ W = \frac{hc}{\lambda_0} \]

### Step-by-step Solution:

1. **Identify the Given Values**:
- Threshold wavelength (λ₀) = 230 nm
- Planck's constant (h) = \(6.626 \times 10^{-34} \, \text{Js}\)
- Speed of light (c) = \(3.00 \times 10^{8} \, \text{m/s}\)

2. **Convert Wavelength to Meters**:
- Since the wavelength is given in nanometers, we need to convert it to meters:
\[ \lambda_0 = 230 \, \text{nm} = 230 \times 10^{-9} \, \text{m} \]

3. **Substitute Values into the Formula**:
- Now, substitute the values of h, c, and λ₀ into the formula:
\[ W = \frac{(6.626 \times 10^{-34} \, \text{Js}) \times (3.00 \times 10^{8} \, \text{m/s})}{230 \times 10^{-9} \, \text{m}} \]

4. **Calculate the Work Function**:
- First, calculate the numerator:
\[ h \cdot c = 6.626 \times 10^{-34} \times 3.00 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{Jm} \]
- Now, divide by the wavelength in meters:
\[ W = \frac{1.9878 \times 10^{-25}}{230 \times 10^{-9}} = 8.64 \times 10^{-19} \, \text{J} \]

5. **Final Result**:
- The work function for the photoelectric emission from the metal is approximately:
\[ W \approx 8.64 \times 10^{-19} \, \text{J} \]