Question

a. Determine the energy, in eV, of a photon with a 550 nm wavelength.

b. Determine the wavelength of a 7.5 keV x-ray photon.

Short answer

a) Energy of the photon is 2.26 eV.

b) Wavelength of the x-ray photon is 0.165 nm.

Step-by-step solution

Step 1. Given information is :a) A photon with 550 nm wavelength.b) A 7.5 keV x-ray photon.

We need to find out :

a) Energy of the photon

b) Wavelength of the x-ray photon

Step 2. Part a) Using expression for energy of photon

$$\begin{gathered} E=hf \\ f=\frac{c}{\lambda } \\ E=h\frac{c}{\lambda } \\ E=\frac{\left(6.63\times {10}^{-34}\right)\left(3\times {10}^{8}m/s\right)}{550\times {10}^{-9}m} \\ E=2.26eV \end{gathered}$$

Step 3. Part b) Using expression of Energy of the photon to find out the wavelength.

$$\begin{gathered} E=\frac{hc}{\lambda } \\ \lambda =\frac{hc}{E} \\ \lambda =\frac{(6.63\times {10}^{-34})\left(3\times {10}^{8}m/s\right)}{7.5\times {10}^3\times 1.6\times {10}^{-19}V} \\ \lambda =0.165nm \end{gathered}$$