The threshold wavelength for ejection of electrons from a metal is 250 nm. The work function for the photoelectric emission from the metal is

Explanation

To find the work function for the photoelectric emission from the 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 wavelength (λ₀) using the formula:
\[ W = \frac{hc}{\lambda_0} \]
where:
- \( W \) is the work function,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)),
- \( c \) is the speed of light (\( 3.00 \times 10^8 \, \text{m/s} \)),
- \( \lambda_0 \) is the threshold wavelength.

2. **Convert the threshold wavelength from nanometers to meters**:
Given that the threshold wavelength \( \lambda_0 \) is 250 nm, we convert this to meters:
\[ \lambda_0 = 250 \, \text{nm} = 250 \times 10^{-9} \, \text{m} \]

3. **Substitute the values into the work function formula**:
Now we can substitute the values of \( h \), \( c \), and \( \lambda_0 \) into the formula:
\[ W = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.00 \times 10^8 \, \text{m/s})}{250 \times 10^{-9} \, \text{m}} \]

4. **Calculate the work function**:
Performing the calculation:
\[ W = \frac{(6.626 \times 10^{-34}) \times (3.00 \times 10^8)}{250 \times 10^{-9}} \]
\[ W = \frac{1.9878 \times 10^{-25}}{250 \times 10^{-9}} = 7.9512 \times 10^{-19} \, \text{J} \]
Rounding to three significant figures, we get:
\[ W \approx 7.95 \times 10^{-19} \, \text{J} \]

### Final Answer:
The work function for the photoelectric emission from the metal is approximately \( 7.95 \times 10^{-19} \, \text{J} \).

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