What is the wavelength of light that is emitted when an excited electron in the hydrogen atom falls from the n = 5 level to the n = 2 level? A) 5.82 × 10^-7 m B) 6.50 × 10^-7 m C) 4.34 × 10^-7 m D) 5.12 × 10^-7 m E) none of these

Question

Quizplus · Accepted Answer

The formula for calculating the wavelength of light emitted from an electron transition in a hydrogen atom is:

λ = (h*c)/(ΔE)

where h is Planck's constant, c is the speed of light, and ΔE is the change in energy between the two levels.

ΔE = E_final - E_initial = (-13.6 eV)*(1/22 - 1/52) = 2.042 eV

Converting to joules:

E = (2.042 eV)*(1.602 × 10^-19 J/eV) = 3.27 × 10^-19 J

Plugging in values:

λ = (6.626 × 10^-34 J*s * 3.00 × 10^8 m/s)/(3.27 × 10^-19 J) = 4.34 × 10^-7 m or 434 nm

Therefore, the correct answer is C.

What Is the Wavelength of Light That Is Emitted When