For two Bohr orbits `n_(1) "and"n_(2)` which follow the relationships, `(n_(2)^(2)=n_(1)^(2))=21 and (n_(2) - n_(1))=3.`
If an electron makes transition from `n_(2) "to" n_(1)` directly then :

The electronic transition from n=2 to n=1 will produce shortest wavelength in:

Find the integral solution for n_(1)n_(2)=2n_(1)-n_(2), " where " n_(1),n_(2) in "integer" .

Find the integral solution for n_(1)n_(2)=2n_(1)-n_(2), " where " n_(1),n_(2) in "integer" .

Find the integral solution for n_(1)n_(2)=2n_(1)-n_(2), " where " n_(1),n_(2) in "integer" .

Find the integral solution for n_(1)n_(2)=2n_(1)-n_(2), " where " n_(1),n_(2) in "integer" .

Consider the follwoing two elerctronic transition possibilites in a hydrogen atom as pictured below : (1) The electron drops from third Bohr's orbit to second Bohr's obit followed with the next transition from second to first Bohr's orbit . (2) The electron drops from third Bohr's orbit to first Bohr's orbit directly . Show that : (a) The sum of the enrgies for the transitions n=3 to n=2 and n=2 to n=1 is equal to the energy of transiton for n=3 to n=1 . (b) Are wavelengths and frequencies of the emitted spectrum also additive in the same way as their energies are ?

Electronic transition in He^(+) ion takes from n_(2) " to " n_(1) shell such that : 2n_(2)+3n_(1)=18 2n_(2)-3n_(1)=6 What will be the total number of photons emitted when electrons transit to n_(1) shell?