Question

A quantum system has three energy levels, so three wavelengths appear in its emission spectrum. The shortest observed wavelength is 278nm ; light with a 434nm wavelength is also observed.

What is the third wavelength?

Answer 1

apply the relation between eenrgy and wavelngth L as E = hc/L

when L = 278 nm

E = 13.6/n^2 = 6.626 e-34 * 3e8/(278 e-9)

E for 13.6/n^2 = 7.15 e -19

n^2 = 13.6*1.6 e-19/7.15 e-19

n = 1.78 (nearly)

similary

when L = 434 nm

E = 13.6/n^2 = 6.626 e-34 * 3e8/(434 e-9)

E for 13.6/n^2 = 4.58 e -19

n^2 = 13.6*1.6 e-19/4.58 e-19

n = 2.2 (nearly)

-----------------------------

for third wavelegngth n = 2.62

so E = 13.6*1.6 e-19/(2.62*2.62)

E =    3.1699 e-19

L = 6.626 e-34* 3e8/(3.169 e-19)

L = 627.64 nm ------<<<<<<<<<<<Third wave length