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In the following Figure is an energy-level diagram for a simple atom. What wavelengths, in nm, appear in the atom鈥檚 (a) emission spectrum and (b) absorption spectrum?

Short Answer

Expert verified

(a) The emission spectrum wavelengths are 21=828.26nm,31=310.6nm,32=497.36nm

(b) The absorption spectrum wavelengths are12=828.26nm,13=310.6nm

Step by step solution

01

Part (a) Step 1: Given information

The given wavelength from the transition is=hc螖贰

02

Part (a) Step 2: Finding the wavelengths of emission spectrum 

The solution can begin with a wavelength equation from the transition.

=hc螖贰21=hcE2E1(transition21)21=6.63103431081.51.610190substitute21=828.26nm31=hcE3E1(transition31)31=6.631034310841.610190substitute31=310.6nm32=hcE3E2(transition32)32=6.631034310841.610191.51.61019substitute32=497.36nm

03

Part (b) Step 1: Given information

The chemical make-up of the gas in the stellar atmosphere determines which wavelengths are absorbed.

04

Part (b) Step 2: Finding the wavelengths of Absorption spectrum

We only have absorption from 12and 13because the atom is in the n=1 state. Because the expressions are the same, the wavelengths are the same.

12:12=828.26nm13:13=310.6nm

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