Find frequency of a photon of energy 3.3 eV?

Options

A. `8xx10^(14)Hz`
B. `8xx10^(12)Hz`
C. `8xx10^(10)Hz`
D. `8xx10^(16)Hz`

Answer

To find the frequency of a photon with an energy of 3.3 eV, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Energy from eV to Joules**:
- The energy given is in electron volts (eV). We need to convert this to joules (J) using the conversion factor:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]
- Therefore, the energy in joules is:
\[ E = 3.3 \text{ eV} \times 1.6 \times 10^{-19} \text{ J/eV} = 5.28 \times 10^{-19} \text{ J} \]

2. **Use Planck's Equation**:
- According to Planck's equation, the energy of a photon is related to its frequency by:
\[ E = h \nu \]
- Where:
- \(E\) is the energy in joules,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \text{ J s}\)),
- \(\nu\) is the frequency in hertz (Hz).

3. **Rearranging the Equation to Solve for Frequency**:
- We can rearrange the equation to solve for frequency (\(\nu\)):
\[ \nu = \frac{E}{h} \]

4. **Substituting the Values**:
- Now, substitute the values of \(E\) and \(h\):
\[ \nu = \frac{5.28 \times 10^{-19} \text{ J}}{6.626 \times 10^{-34} \text{ J s}} \]

5. **Calculating the Frequency**:
- Performing the division:
\[ \nu \approx 7.97 \times 10^{14} \text{ Hz} \]
- Rounding to two decimal places, we can say:
\[ \nu \approx 8.0 \times 10^{14} \text{ Hz} \]

### Final Answer:
The frequency of the photon with an energy of 3.3 eV is approximately \(8.0 \times 10^{14} \text{ Hz}\).

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