What is the energy in joule of photon of light whose wave length is 15 x` 10^5 `nm

Options

A. `1.3xx10^(21)`
B. `1.3xx10^(-20)`
C. `1.3xx10^(-22)`
D. `1.3xx10^(-23)`

Explanation

To find the energy of a photon of light with a given wavelength, we can use the formula:

\[ E = \frac{hc}{\lambda} \]

where:
- \( E \) is the energy of the photon in joules,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)),
- \( c \) is the speed of light (\( 3.0 \times 10^{8} \, \text{m/s} \)),
- \( \lambda \) is the wavelength in meters.

### Step 1: Convert the wavelength from nanometers to meters
The given wavelength is \( 15 \times 10^5 \, \text{nm} \). To convert nanometers to meters, we use the conversion factor \( 1 \, \text{nm} = 10^{-9} \, \text{m} \).

\[ \lambda = 15 \times 10^5 \, \text{nm} \times 10^{-9} \, \text{m/nm} = 15 \times 10^{-4} \, \text{m} \]

### Step 2: Substitute the values into the energy formula
Now we can substitute the values of \( h \), \( c \), and \( \lambda \) into the energy formula.

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.0 \times 10^{8} \, \text{m/s})}{15 \times 10^{-4} \, \text{m}} \]

### Step 3: Calculate the energy
First, calculate the numerator:

\[ 6.626 \times 10^{-34} \times 3.0 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J m} \]

Now, divide by the wavelength:

\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{15 \times 10^{-4} \, \text{m}} = \frac{1.9878 \times 10^{-25}}{15 \times 10^{-4}} = 1.3252 \times 10^{-22} \, \text{J} \]

### Step 4: Round the result
Rounding \( 1.3252 \times 10^{-22} \, \text{J} \) gives approximately:

\[ E \approx 1.3 \times 10^{-22} \, \text{J} \]

Thus, the energy of the photon is approximately \( 1.3 \times 10^{-22} \, \text{J} \).

### Final Answer:
The energy of the photon is \( 1.3 \times 10^{-22} \, \text{J} \).

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