To find the frequency of a photon with an energy of 3.3 eV, we can follow these steps:
### Step 1: Understand the relationship between energy and frequency
The energy \( E \) of a photon is given by the formula:
\[
E = h \nu
\]
where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.63 \times 10^{-34} \, \text{J s} \)),
- \( \nu \) is the frequency of the photon.
### Step 2: Rearrange the formula to solve for frequency
To find the frequency \( \nu \), we can rearrange the formula:
\[
\nu = \frac{E}{h}
\]
### Step 3: Convert energy from electron volts to joules
The energy given is in electron volts (eV). We need to convert this to joules (J). The conversion factor is:
\[
1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J}
\]
Thus, for \( 3.3 \, \text{eV} \):
\[
E = 3.3 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 5.28 \times 10^{-19} \, \text{J}
\]
### Step 4: Substitute the values into the frequency formula
Now we can substitute the values of \( E \) and \( h \) into the frequency formula:
\[
\nu = \frac{5.28 \times 10^{-19} \, \text{J}}{6.63 \times 10^{-34} \, \text{J s}}
\]
### Step 5: Calculate the frequency
Calculating this gives:
\[
\nu \approx \frac{5.28}{6.63} \times 10^{15} \, \text{s}^{-1}
\]
\[
\nu \approx 0.797 \times 10^{15} \, \text{s}^{-1} \approx 7.97 \times 10^{14} \, \text{Hz}
\]
### Final Answer
The frequency of the photon is approximately:
\[
\nu \approx 7.97 \times 10^{14} \, \text{Hz}
\]
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