Frequency of photon having energy 66 eV is

Options

A. `8 xx 10^(-15) Hz`
B. `12 xx 10^(-15) Hz`
C. `16 xx 10^(15) Hz`
D. None of these

Answer

To find the frequency of a photon with an energy of 66 eV, we can use the formula that relates energy (E) and frequency (ν):

### Step-by-Step Solution:

1. **Understand the relationship between energy and frequency**:
The energy of a photon is given by the equation:
\[ E = h \cdot \nu \]
where \(E\) is the energy, \(h\) is Planck's constant, and \(\nu\) is the frequency.

2. **Rearrange the formula to solve for frequency**:
To find the frequency, we can rearrange the formula:
\[ \nu = \frac{E}{h} \]

3. **Convert energy from electron volts to joules**:
The energy given is in electron volts (eV). To convert eV to joules (J), we use the conversion factor:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]
Therefore, for 66 eV:
\[ E = 66 \text{ eV} \times 1.6 \times 10^{-19} \text{ J/eV} = 1.056 \times 10^{-17} \text{ J} \]

4. **Use the value of Planck's constant**:
The value of Planck's constant \(h\) is approximately:
\[ h = 6.63 \times 10^{-34} \text{ J s} \]

5. **Substitute the values into the frequency formula**:
Now we can substitute the values of \(E\) and \(h\) into the frequency formula:
\[ \nu = \frac{1.056 \times 10^{-17} \text{ J}}{6.63 \times 10^{-34} \text{ J s}} \]

6. **Calculate the frequency**:
Performing the division:
\[ \nu \approx 1.59 \times 10^{16} \text{ Hz} \]

### Final Answer:
The frequency of the photon having energy 66 eV is approximately:
\[ \nu \approx 1.59 \times 10^{16} \text{ Hz} \]