Threshold wavelength for photoelectric effect on sodium is `5000 Å` . Its work function is

Options

A. `4 xx 10^(-19) J`
B. `1 J`
C. `2 xx 10^(-19)` J
D. `3 xx 10^(-19)` J

Answer

To find the work function of sodium given its threshold wavelength for the photoelectric effect, we can follow these steps:

### Step 1: Understand the relationship between work function and wavelength
The work function (φ) can be calculated using the formula:
\[ \phi = \frac{hc}{\lambda_0} \]
where:
- \( \phi \) = work function
- \( h \) = Planck's constant (\(6.63 \times 10^{-34} \, \text{Js}\))
- \( c \) = speed of light (\(3 \times 10^8 \, \text{m/s}\))
- \( \lambda_0 \) = threshold wavelength (in meters)

### Step 2: Convert the threshold wavelength from angstroms to meters
Given that the threshold wavelength is \(5000 \, \text{Å}\):
\[ \lambda_0 = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

### Step 3: Substitute the values into the work function formula
Now substituting the values of \(h\), \(c\), and \(\lambda_0\) into the formula:
\[ \phi = \frac{(6.63 \times 10^{-34} \, \text{Js}) \times (3 \times 10^8 \, \text{m/s})}{5 \times 10^{-7} \, \text{m}} \]

### Step 4: Calculate the numerator
Calculating the numerator:
\[ 6.63 \times 3 = 19.89 \quad \text{(approximately 20)} \]
Thus, the numerator becomes:
\[ 19.89 \times 10^{-34 + 8} = 19.89 \times 10^{-26} \, \text{Jm} \]

### Step 5: Calculate the work function
Now, we can calculate:
\[ \phi = \frac{19.89 \times 10^{-26}}{5 \times 10^{-7}} = \frac{19.89}{5} \times 10^{-26 + 7} = 3.978 \times 10^{-19} \, \text{J} \]
This can be approximated to:
\[ \phi \approx 4 \times 10^{-19} \, \text{J} \]

### Conclusion
Thus, the work function of sodium is approximately:
\[ \phi \approx 4 \times 10^{-19} \, \text{J} \]