# Origin of Spectra

So long an electron revolves around the nucleus in a particular orbit, its energy remains constant. When an electron absorbs energy, it suddenly jumps into a higher energy level.

Since an electron can not stay in this excited state forever, it jumps back into a lower energy level. The excess energy is radiated as a single photon.

The energy of the photon is equal to the difference between the energies of the two orbits.

$\displaystyle \Delta E = 13.6Z^2 (\frac{1}{n_i^2} – \frac{1}{n_f^2})$

Here Z = atomic number

ni = principal quantum number of initial orbit.

nf = principal quantum number of final orbit.

The above expression is valid only for hydrogen or hydrogen like atom.

Illustration  : Find the orbital magnetic dipole moment of the electron in a hydrogen atom.

Solution : The orbiting electron behaves as a current loop.

The equivalent current

i = net charge / Time of revolution = e/T = e ν

Now, magnetic dipole moment μ = I A

A = area of the loop = π r2

⇒ μ = (e ν) (π r2)

⇒ μ = πe r2 ν

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