Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 4 to the n = 1 principal energy level.Recall that for hydrogen E_n = -2.18 × 10^-18 J(1/n²) A)1.35 × 10^-51/s B)1.03 × 10⁸/s C)2.06 × 10¹⁴/s D)8.22 × 10¹⁴/s E)3.08 × 10¹⁵/s

Question

Quizplus · Accepted Answer

The frequency of the emitted light is given by:
v = ΔE / h
where ΔE is the difference in energy between the two levels and h is Planck's constant. 
Using the formula provided, we can find the energy difference between the n = 4 and n = 1 levels:
ΔE = (2.18 × 10^-18 J) * (1/1^2 - 1/4^2) = 2.04 × 10^-18 J
Substituting this back into the equation for frequency, we get:
v = (2.04 × 10^-18 J) / (6.626 × 10^-34 J*s) = 3.08 × 10^15 Hz or s^-1.
Therefore, the best choice is E, which corresponds to 3.08 × 10^15 S-1 or Hz.

Calculate the Frequency of the Light Emitted by a Hydrogen