What is the wavelength of a photon with energy $E=3.03\times 10^{-19}\text{ J}$? (Given: $h=6.63\times 10^{-34}\text{ Js}$, $c=3\times 10^8\text{ m/s}$)

Solution

1. The relationship is $\lambda =\frac{hc}{E}$.
2. Substitute the values: $\lambda =\frac{6.63\times 10^{-34}\times 3\times 10^8}{3.03\times 10^{-19}}$.
3. $\lambda \approx 6.56\times 10^{-7}\text{ m}$.
4. Convert to nanometers: $6.56\times 10^{-7}\text{ m}=656\text{ nm}$.
5. Hence the answer is (A).