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 wavelength of light emitted during the transition from the n=5 to the n=2 level in hydrogen can be calculated using the Rydberg formula: 
1/λ = R(1/nf^2 - 1/ni^2)
where R is the Rydberg constant, nf is the final energy level (n=2), and ni is the initial energy level (n=5). Plugging in the values: 
1/λ = R(1/2^2 - 1/5^2)
1/λ = R(9/100 - 4/25)
1/λ = R(1/100)
λ = 100R = 100(1.0968 x 10^7 m^-1) = 1.0968 x 10^9 m^-1 = 4.34 x 10^-7 m or 434 nm. 
Therefore, the correct answer is choice C.

What Is the Wavelength of Light That Is Emitted When