Question

Find the wavelength of a photon that has an energy of 12.4eV

Answer 1

To find the wavelength of a photon given its energy, you can use the relationship between energy and wavelength given by the equation:

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

Where:
- \( E \) is the energy of the photon (in joules),
- \( h \) is the Planck constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \( c \) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \( \lambda \) is the wavelength (in meters).

First, convert the energy from electronvolts to joules. The conversion factor is:

\[
1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J}
\]

Thus,

\[
E = 12.4 \, \text{eV} \times 1.602 \times 10^{-19} \, \text{J/eV} = 1.987 \times 10^{-18} \, \text{J}
\]

Next, rearrange the equation to solve for the wavelength \( \lambda \):

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

Substituting in the values:

\[
\lambda = \frac{(6.626 \times 10^{-34} \, \text{Js})(3.00 \times 10^8 \, \text{m/s})}{1.987 \times 10^{-18} \, \text{J}}
\]

Calculating this gives:

\[
\lambda = \frac{1.9878 \times 10^{-25} \, \text{J m}}{1.987 \times 10^{-18} \, \text{J}} \approx 1.001 \times 10^{-7} \, \text{m}
\]

Converting this into nanometers (1 nm = \( 10^{-9} \, \text{m} \)):

\[
\lambda \approx 100.1 \, \text{nm}
\]

Thus, the wavelength of the photon with an energy of 12.4 eV is approximately **100 nm**.