The frequency of a photon associated with an energy of `3.31eV` is ( given `h=6.62xx10^(-34) Js`)

Options

A. `0.8xx10^(15) Hz`
B. `1.6xx10^(15) Hz`
C. `3.2xx10^(15) Hz`
D. `8.0xx10^(15) Hz`

Explanation

To find the frequency of a photon associated with an energy of \(3.31 \, \text{eV}\), we can use the relationship between energy (E), frequency (ν), and Planck's constant (h). The formula is given by:

\[ E = h \cdot \nu \]

Where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant,
- \(\nu\) is the frequency of the photon.

### Step 1: Convert Energy from eV to Joules
First, we need to convert the energy from electron volts (eV) to joules (J). The conversion factor is:

\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]

So, we calculate:

\[ E = 3.31 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 5.296 \times 10^{-19} \, \text{J} \]

### Step 2: Use the Energy-Frequency Relationship
Now that we have the energy in joules, we can rearrange the formula to solve for frequency:

\[ \nu = \frac{E}{h} \]

Substituting the values we have:

\[ \nu = \frac{5.296 \times 10^{-19} \, \text{J}}{6.62 \times 10^{-34} \, \text{Js}} \]

### Step 3: Calculate the Frequency
Now we perform the calculation:

\[ \nu = \frac{5.296 \times 10^{-19}}{6.62 \times 10^{-34}} \approx 7.99 \times 10^{14} \, \text{Hz} \]

### Final Result
Thus, the frequency of the photon associated with an energy of \(3.31 \, \text{eV}\) is approximately:

\[ \nu \approx 7.99 \times 10^{14} \, \text{Hz} \]

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