What is the energy in joule of photon of light whose wave length is 12 x` 10^3 `nm

Options

A. 1.5 x `10^(-19)`
B. 2.5 x `10^(-19)`
C. 1.6 x `10^(-20)`
D. None of these

Answer

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 (\(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength (in meters).

### Step-by-Step Solution:

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

Given:
\[ \lambda = 12 \times 10^3 \, \text{nm} \]

To convert nanometers to meters, we use the conversion factor \(1 \, \text{nm} = 10^{-9} \, \text{m}\):
\[ \lambda = 12 \times 10^3 \, \text{nm} = 12 \times 10^3 \times 10^{-9} \, \text{m} = 12 \times 10^{-6} \, \text{m} \]

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

Using the values of \(h\), \(c\), and \(\lambda\):
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{12 \times 10^{-6} \, \text{m}} \]

**Step 3: Calculate the energy.**

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

Now, divide by the wavelength:
\[ E = \frac{1.9878 \times 10^{-25}}{12 \times 10^{-6}} = \frac{1.9878 \times 10^{-25}}{1.2 \times 10^{-5}} = 1.6565 \times 10^{-20} \, \text{J} \]

**Step 4: Round the result.**

Rounding to two significant figures, we get:
\[ E \approx 1.6 \times 10^{-20} \, \text{J} \]

### Final Answer:
The energy of the photon is approximately \(1.6 \times 10^{-20} \, \text{J}\).

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