The energy of a photon of radiation having wavelength 300 nm is,

Options

A. `6.63xx10^(29)J`
B. `6.63xx10^(-19)J`
C. `6.63xx10^(-28)J`
D. `6.63xx10^(-17)J`

Explanation

To find the energy of a photon with a wavelength of 300 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 (\( 3.00 \times 10^{8} \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the radiation in meters.

**Step 1: Convert the wavelength from nanometers to meters.**
- Given wavelength \( \lambda = 300 \, \text{nm} \).
- Since \( 1 \, \text{nm} = 10^{-9} \, \text{m} \), we convert:
\[ \lambda = 300 \, \text{nm} = 300 \times 10^{-9} \, \text{m} = 3.00 \times 10^{-7} \, \text{m} \]

**Step 2: Substitute the values into the energy formula.**
- Now we substitute \( h \), \( c \), and \( \lambda \) into the equation:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.00 \times 10^{8} \, \text{m/s})}{3.00 \times 10^{-7} \, \text{m}} \]

**Step 3: Calculate the energy.**
- Performing the calculation:
\[ E = \frac{(6.626 \times 10^{-34}) \times (3.00 \times 10^{8})}{3.00 \times 10^{-7}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{3.00 \times 10^{-7}} = 6.626 \times 10^{-19} \, \text{J} \]

**Step 4: Final result.**
- The energy of the photon is:
\[ E \approx 6.63 \times 10^{-19} \, \text{J} \]

Thus, the correct option is option number B.

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