Calculate the wavelength of light associated with the transition from n = 1 to n = 3 in the hydrogen atom.
A) 103 nm
B) 155 nm
C) 646 nm
D) 971 nm
E) 136 nm

Question

Quizplus · Accepted Answer

The energy of a photon is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. The energy difference between the n = 1 and n = 3 levels in the hydrogen atom is given by:ΔE = E3 - E1 = -13.6 eV * (1/3^2 - 1/1^2) = -10.2 eVConverting this energy to joules:ΔE = -10.2 eV * (1.602 x 10^-19 J/eV) = -1.63 x 10^-18 JUsing the equation E = hc/λ, we can solve for the wavelength:λ = hc/ΔE = (6.626 x 10^-34 J s) * (3 x 10^8 m/s) / (-1.63 x 10^-18 J) = 1.22 x 10^-7 m = 122 nmTherefore, the wavelength of light associated with the transition from n = 1 to n = 3 in the hydrogen atom is 122 nm, which is closest to choice A, 103 nm.

Calculate the Wavelength of Light Associated with the Transition from N