Question

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?

Answer 1

Answer:
`\lambda _3=(\lambda )/(3)`

Step-by-step explanation:

Given

`E_3-E_2=(hc)/(\lambda )`

also
`E_2-E_1=2\left ( E_3-E_2\right )`

Let wavelength produce during transition from 2 to 1 is
`\lambda_0`

`(hc)/(\lambda _0)=2(hc)/(\lambda )`

`\lambda _0=(\lambda )/(2)`

For
`E_3 to E_1 transition`

`E_3-E_1=E_3-E_2+E_2-E_1`

`E_3-E_1=(hc)/(\lambda )+2(hc)/(\lambda )`

`(hc)/(\lambda _3)=3(hc)/(\lambda )`

`\lambda _3=(\lambda )/(3)`