Monochromatic photons of energy 3.3 eV are incident on a photo sensitive surface of work function 2.4 eV. Calculate the threshold frequency of incident radiation.

Options

A. `6.82 xx 10^(14) Hz`
B. `5.82 xx 10^(14) Hz`
C. `7.82 xx 10^(14) Hz`
D. `10.82 xx 10^(14) Hz`

Answer

To solve the problem, we need to calculate the threshold frequency of the incident radiation using the work function of the photosensitive surface. Here’s a step-by-step solution:

### Step 1: Understand the Relationship
The threshold frequency (ν₀) is related to the work function (Φ) of the material by the equation:
\[ E = hν₀ \]
where:
- \( E \) is the energy required to eject an electron (the work function).
- \( h \) is Planck's constant.
- \( ν₀ \) is the threshold frequency.

### Step 2: Identify Given Values
From the problem, we have:
- Work function \( Φ = 2.4 \, \text{eV} \)
- Planck's constant \( h = 6.626 \times 10^{-34} \, \text{Js} \)

### Step 3: Convert Work Function to Joules
To use the equation, we need to convert the work function from electron volts to joules. The conversion factor is:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
Thus,
\[ Φ = 2.4 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 3.84 \times 10^{-19} \, \text{J} \]

### Step 4: Rearrange the Equation for Threshold Frequency
We can rearrange the equation to solve for the threshold frequency:
\[ ν₀ = \frac{Φ}{h} \]

### Step 5: Substitute the Values
Now we can substitute the values we have into the equation:
\[ ν₀ = \frac{3.84 \times 10^{-19} \, \text{J}}{6.626 \times 10^{-34} \, \text{Js}} \]

### Step 6: Calculate the Threshold Frequency
Perform the calculation:
\[ ν₀ = \frac{3.84 \times 10^{-19}}{6.626 \times 10^{-34}} \approx 5.79 \times 10^{14} \, \text{Hz} \]

### Step 7: Round Off the Answer
Rounding off to two decimal places gives:
\[ ν₀ \approx 5.82 \times 10^{14} \, \text{Hz} \]

### Final Answer
The threshold frequency of the incident radiation is approximately:
\[ ν₀ \approx 5.82 \times 10^{14} \, \text{Hz} \]