The frequency of a photon , having energy `100 eV is ( h = 6.610^(-34) J - sec)`

Options

A. `2.42 xx 10^(26) Hz`
B. `2.42 xx 10^(16) Hz`
C. `2.42 xx 10^(12) Hz`
D. `2.42 xx 10^(9) Hz`

Explanation

To find the frequency of a photon with an energy of 100 eV, we can use the formula that relates energy (E) to frequency (ν):

\[ E = h \nu \]

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
The energy given is in electron volts (eV), and we need to convert it to joules (J). The conversion factor is:

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

So, for 100 eV:

\[ E = 100 \text{ eV} \times 1.6 \times 10^{-19} \text{ J/eV} = 1.6 \times 10^{-17} \text{ J} \]

### Step 2: Use the Energy-Frequency Relation
Now that we have the energy in joules, we can rearrange the formula \( E = h \nu \) to solve for frequency \( \nu \):

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

### Step 3: Substitute the Values
We know:
- \( E = 1.6 \times 10^{-17} \text{ J} \)
- \( h = 6.63 \times 10^{-34} \text{ J s} \)

Substituting these values into the equation gives:

\[ \nu = \frac{1.6 \times 10^{-17} \text{ J}}{6.63 \times 10^{-34} \text{ J s}} \]

### Step 4: Calculate the Frequency
Now we perform the calculation:

\[ \nu = \frac{1.6}{6.63} \times 10^{(−17 + 34)} \]

Calculating \( \frac{1.6}{6.63} \):

\[ \nu \approx 0.241 \times 10^{17} \]

This can be expressed as:

\[ \nu \approx 2.41 \times 10^{16} \text{ Hz} \]

### Final Answer
The frequency of the photon with an energy of 100 eV is approximately:

\[ \nu \approx 2.41 \times 10^{16} \text{ Hz} \]

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