Question

A certain atom has only three energy levels. From lowest to highest energy, these levels are denoted n = 1, n = 2, and n = 3. When the atom transitions from the n = 3 level to the n = 2 level, it emits a photon of wavelength 800 nm. When the atom transitions from the n = 2 level to the n = 1 level, it emits a photon of wavelength 200 nm. What is the wavelength of the photon emitted when the atom transitions from the n = 3 level to the n = 1 level?A. 1000 nm
B. 600 nm
C. 500 nm
D. 160 nm

Answer 1

Answer:

D. 160 nm

Explanation:

The energy released from n = 3 to n = 1 must be equal to the sum of energies released from n = 3 to n = 2 and from n = 2 to n = 1. Therefore,

Energy of Photon from 3 to 1 = Energy of Photon from 3 to 2 + Energy of Photon from 2 to 1

$\frac{hc}{\lambda} = \frac{hc}{\lambda_{1}} + \frac{hc}{\lambda_{2}}\\\\\frac{1}{\lambda} = \frac{1}{\lambda_{1}} + \frac{1}{\lambda_{2}}$

where,

λ = wavelength of photon released from 3 to 1 = ?

λ₁ = wavelength of photon released from 3 to 2 = 800 nm

λ₂ = wavelength of photon released from 2 to 1 = 200 nm

Therefore,

$\frac{1}{\lambda} = \frac{1}{800\ nm} + \frac{1}{200\ nm}\\\\\frac{1}{\lambda} = 0.00625 nm^{-1}\\\\\lambda = \frac{1}{0.00625 nm^{-1}}\\\\\lambda = 160 nm$

Therefore, the correct option is:

D. 160 nm