The threshold wavelength for ejection of electrons from a metal is 330 nm. The work function for the photoelectric emission from the metal is

Options

A. 6.0×`10^(−19)`J
B. 6.0×`10^(−12)`J
C. 1.2×`10^(−19)`J
D. 1.2×`10^(−18)`J

Explanation

To find the work function for the photoelectric emission from a metal given the threshold wavelength, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between work function and wavelength**:
The work function (W) can be expressed in terms of the threshold frequency (ν₀) using the equation:
\[ W = h \nu_0 \]
where \( h \) is Planck's constant.

2. **Relate frequency to wavelength**:
The threshold frequency can also be related to the threshold wavelength (λ₀) using the equation:
\[ \nu_0 = \frac{c}{\lambda_0} \]
where \( c \) is the speed of light.

3. **Substitute the expression for frequency into the work function equation**:
By substituting the expression for frequency into the work function equation, we get:
\[ W = h \frac{c}{\lambda_0} \]

4. **Convert the threshold wavelength from nanometers to meters**:
Given that the threshold wavelength \( \lambda_0 \) is 330 nm, we convert it to meters:
\[ \lambda_0 = 330 \, \text{nm} = 330 \times 10^{-9} \, \text{m} \]

5. **Substitute known values into the equation**:
Now we can substitute the values into the equation for work function:
- Planck's constant \( h = 6.626 \times 10^{-34} \, \text{J s} \)
- Speed of light \( c = 3.00 \times 10^{8} \, \text{m/s} \)
\[ W = \left(6.626 \times 10^{-34} \, \text{J s}\right) \left(\frac{3.00 \times 10^{8} \, \text{m/s}}{330 \times 10^{-9} \, \text{m}}\right) \]

6. **Calculate the work function**:
First, calculate the frequency:
\[ \nu_0 = \frac{3.00 \times 10^{8}}{330 \times 10^{-9}} = 9.09 \times 10^{14} \, \text{Hz} \]
Now calculate the work function:
\[ W = 6.626 \times 10^{-34} \times 9.09 \times 10^{14} = 6.02 \times 10^{-19} \, \text{J} \]

### Final Answer:
The work function for the photoelectric emission from the metal is approximately \( 6.02 \times 10^{-19} \, \text{J} \).