Calculate the wavelength of a photon with energy 2.45 eV.
5.09 * 10^-7
To calculate the wavelength of a photon, we can use the equation:
\[E = \frac{hc}{\lambda}\]
where:
- \(E\) is the energy of the photon,
- \(h\) is the Planck's constant (\(6.62607015 \times 10^{-34} \, \text{J} \cdot \text{s}\)),
- \(c\) is the speed of light (\(2.998 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength of the photon.
In this case, the energy of the photon is given as 2.45 eV. Recall that 1 eV is equal to \(1.60218 \times 10^{-19} \, \text{J}\). We can convert the energy from eV to joules:
\[2.45 \, \text{eV} \times (1.60218 \times 10^{-19} \, \text{J/eV}) = 3.93 \times 10^{-19} \, \text{J}\]
Now, we can rearrange the equation to solve for the wavelength:
\[\lambda = \frac{hc}{E}\]
Plugging in the values:
\[\lambda = \frac{(6.62607015 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (2.998 \times 10^8 \, \text{m/s})}{3.93 \times 10^{-19} \, \text{J}}\]
Simplifying this calculation will give us the wavelength of the photon.