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Wave Optics

Question
CBSEENPH12040030

The ionisation energy of the electron in the hydrogen atom in its ground state is 13.6 eV. The atoms are excited to higher energy levels to emit radiations of 6 wavelengths. Maximum wavelength of emitted radiation corresponds to the transition between

  • n = 3 to n =2 states

  • n = 3 to n = 1 states

  • n = 2 to n = 1 states

  • n = 4 to n =3 states

Solution

D.

n = 4 to n =3 states

Number of spectral lines obtained due to transition of electron from nth orbit to lower orbit is N = n(n-1)/2 and for maximum wavelength, the difference between the orbits of the series should be minimum
Number of spectral lines N = n (n-1)/2
= n (n-1)/2 = 6
= n2-n-12 = 0
(n-4)(n+3) = 0
n=4
Now as the first line of the series has the maximum wavelength, therefore, electrons jump from the 4th orbit to the third orbit.