A wave has a frequency of `3 xx 10^(15) sec^(-1)`. The energy of that photon is

Options

A. `1.6 xx 10^(-12)` erg
B. `3.2 xx 10^(-11)` erg
C. `2.0 xx 10^(-11)` erg
D. `3 xx 10^(15)` erg

Answer

To find the energy of a photon given its frequency, we can use the formula:

\[ E = h \nu \]

Where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant, approximately \( 6.626 \times 10^{-34} \, \text{J s} \),
- \( \nu \) (nu) is the frequency of the wave.

### Step-by-Step Solution:

**Step 1: Identify the given frequency.**
The frequency \( \nu \) is given as:
\[ \nu = 3 \times 10^{15} \, \text{s}^{-1} \]

**Step 2: Use Planck's constant.**
Using the value of Planck's constant:
\[ h = 6.626 \times 10^{-34} \, \text{J s} \]

**Step 3: Substitute the values into the energy formula.**
Now, substitute the values of \( h \) and \( \nu \) into the formula:
\[ E = (6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{15} \, \text{s}^{-1}) \]

**Step 4: Perform the multiplication.**
Calculating the energy:
\[ E = 6.626 \times 3 \times 10^{-34} \times 10^{15} \]
\[ E = 19.878 \times 10^{-19} \, \text{J} \]
\[ E \approx 1.99 \times 10^{-18} \, \text{J} \]

**Step 5: Convert the energy from joules to electronvolts.**
To convert joules to electronvolts, we use the conversion factor:
\[ 1 \, \text{J} = 6.242 \times 10^{18} \, \text{eV} \]
Thus,
\[ E \approx 1.99 \times 10^{-18} \, \text{J} \times 6.242 \times 10^{18} \, \text{eV/J} \]
\[ E \approx 12.43 \, \text{eV} \]

### Final Answer:
The energy of the photon is approximately \( 12.43 \, \text{eV} \).