What is the energy in joule of photon of light whose wave length is 15 x` 10^3 `nm

Options

A. 3.5 x `10^(-19)`
B. 1.3 x `10^(-20)`
C. 2.5 x `10^(-19)`
D. None of these

Explanation

To find the energy of a photon of light with a wavelength of \(15 \times 10^3\) nm, we can use the formula:

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

where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\)),
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters.

### Step-by-Step Solution

**Step 1: Convert the wavelength from nanometers to meters.**

Given:
\[ \lambda = 15 \times 10^3 \, \text{nm} \]

To convert nanometers to meters, we use the conversion factor \(1 \, \text{nm} = 10^{-9} \, \text{m}\):
\[ \lambda = 15 \times 10^3 \, \text{nm} \times 10^{-9} \, \text{m/nm} = 15 \times 10^{-6} \, \text{m} \]

**Step 2: Substitute the values into the energy formula.**

Now we can substitute \(h\), \(c\), and \(\lambda\) into the energy formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{15 \times 10^{-6} \, \text{m}} \]

**Step 3: Calculate the energy.**

Calculating the numerator:
\[ 6.626 \times 10^{-34} \times 3 \times 10^8 = 1.9878 \times 10^{-25} \, \text{J m} \]

Now, divide by the wavelength:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{15 \times 10^{-6} \, \text{m}} = \frac{1.9878 \times 10^{-25}}{15 \times 10^{-6}} = 1.3252 \times 10^{-20} \, \text{J} \]

**Step 4: Round the result.**

Rounding the result gives:
\[ E \approx 1.3 \times 10^{-20} \, \text{J} \]

### Final Answer
The energy of the photon is approximately \(1.3 \times 10^{-20} \, \text{J}\).

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