We’re being asked to calculate for the wavelength of light emitted by an electron to transition from n=5 to n = 2.

We’re going to use the **Balmer Equation** which relates wavelengths to a photon’s electronic transitions.

$\overline{)\frac{\mathbf{1}}{\mathbf{\lambda}}{\mathbf{=}}{{\mathbf{RZ}}}^{{\mathbf{2}}}\left(\frac{\mathbf{1}}{{{\mathbf{n}}^{\mathbf{2}}}_{\mathbf{final}}}\mathbf{-}\frac{\mathbf{1}}{{{\mathbf{n}}^{\mathbf{2}}}_{\mathbf{initial}}}\right)}$

λ = wavelength, m

R = Rydberg constant = 1.097x10^{7} m^{-1}

Z = atomic number of the element

n_{initial }= initial energy level

n_{final} = final energy level

**Calculate the ****wavelength of light emitted ****(****λ):**

What is the wavelength (in nm) of light emitted from a hydrogen atom when an electron falls from the n = 5 to n = 2 energy level?

a. 780

b. 656

c. 486

d. 434

e. 308