The energy spacing between levels 1 and 2 is twice that between 2 and 3. If an electron makes a transition from level 3 to level 2, the radiation of wavelength λ is emitted. What possible radiation wavelengths might be produced by other transitions among the three energy levels?

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nuuk nuuk · Answer 1 · 2019-08-09T10:00:06+02:00

Answer:[tex]\lambda _3=\frac{\lambda }{3}[/tex]

Explanation:

Given

[tex]E_3-E_2=\frac{hc}{\lambda }[/tex]

also [tex]E_2-E_1=2\left ( E_3-E_2\right )[/tex]

Let wavelength produce during transition from 2 to 1 is [tex]\lambda_0[/tex]

[tex]\frac{hc}{\lambda _0}=2\frac{hc}{\lambda }[/tex]

[tex]\lambda _0=\frac{\lambda }{2}[/tex]

For [tex]E_3 to E_1 transition [/tex]

[tex]E_3-E_1=E_3-E_2+E_2-E_1[/tex]

[tex]E_3-E_1=\frac{hc}{\lambda }+2\frac{hc}{\lambda }[/tex]

[tex]\frac{hc}{\lambda _3}=3\frac{hc}{\lambda }[/tex]

[tex]\lambda _3=\frac{\lambda }{3}[/tex]