What is the work function of a substance if photoelectrons are just ejected for a monochromatic light of wavelength
`lambda = 3300` Å (answer in eV) ?

Options

A. 3.75
B. 3.25
C. 1.36
D. 0.75

Explanation

To find the work function of a substance when photoelectrons are just ejected for monochromatic light of wavelength \( \lambda = 3300 \) Å, we can follow these steps:

### Step 1: Convert Wavelength to Meters
The given wavelength is in Angstroms (Å). We need to convert it to meters for our calculations.

\[ \lambda = 3300 \, \text{Å} = 3300 \times 10^{-10} \, \text{m} \]

### Step 2: Calculate the Frequency
Using the relationship between the speed of light (c), wavelength (\( \lambda \)), and frequency (\( \nu \)), we can calculate the frequency of the light.

\[ \nu = \frac{c}{\lambda} \]

Where:
- \( c = 3 \times 10^8 \, \text{m/s} \)
- \( \lambda = 3300 \times 10^{-10} \, \text{m} \)

Substituting the values:

\[ \nu = \frac{3 \times 10^8}{3300 \times 10^{-10}} \approx 9.09 \times 10^{14} \, \text{Hz} \]

### Step 3: Calculate the Energy of the Photons
The energy of the photons can be calculated using the formula:

\[ E = h \nu \]

Where:
- \( h = 6.626 \times 10^{-34} \, \text{J s} \)

Substituting the values:

\[ E = 6.626 \times 10^{-34} \times 9.09 \times 10^{14} \approx 6.02 \times 10^{-19} \, \text{J} \]

### Step 4: Convert Energy to Electron Volts
To find the work function in electron volts (eV), we convert the energy from joules to electron volts using the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \).

\[ \text{Work function} = \frac{6.02 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 3.76 \, \text{eV} \]

### Final Answer
The work function of the substance is approximately \( 3.76 \, \text{eV} \).

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