If the threshold wavelength of light for photoelectric effect from sodium surface is 6800 Å then, the work function of sodium is

Options

A. 1.8 Ev
B. 2.9eV
C. 1.1 Ev
D. 4.7 Ev

Explanation

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

### Step-by-Step Solution:

1. **Understand the relationship between work function and threshold wavelength**:
The work function (ϕ) of a material can be calculated using the formula:
\[ \phi = \frac{hc}{\lambda} \]
where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the threshold wavelength.

2. **Convert the threshold wavelength from angstroms to meters**:
The given threshold wavelength is \( 6800 \, \text{Å} \).
\[ 1 \, \text{Å} = 10^{-10} \, \text{m} \]
Therefore,
\[ \lambda = 6800 \, \text{Å} = 6800 \times 10^{-10} \, \text{m} = 6.8 \times 10^{-7} \, \text{m} \]

3. **Calculate \( hc \)**:
We can calculate \( hc \) in electron volts using the known value:
\[ hc \approx 12400 \, \text{eV} \cdot \text{Å} \]

4. **Substitute the values into the work function formula**:
Now, substituting the values into the formula:
\[ \phi = \frac{12400 \, \text{eV} \cdot \text{Å}}{6800 \, \text{Å}} \]

5. **Perform the calculation**:
\[ \phi = \frac{12400}{6800} \, \text{eV} \approx 1.8235 \, \text{eV} \]
Rounding this, we find:
\[ \phi \approx 1.8 \, \text{eV} \]

### Final Answer:
The work function of sodium is approximately \( 1.8 \, \text{eV} \).

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