Question

An electron in a hydrogen atom in the level n = 5 undergoes a transition to n = 3.

Which of the following transitions ( circle any/all correct answer(s) ) would be lower energy?

n=2 to n=1

n=3 to n=1

n=5 to n=4

n=4 to n=2

n=6 to n=4

Answer 1

The complete step wise calculation is given as below:-

Energy of the hydrogen atom is givenby E = K = 0 where, ne energy level and k= constant. It is given that ni - 5 =initial level n = 3 = Final level. Theme = k [ ne more = k [ 55 - 25) on E = 0.071* — @

Further case- mi=2, nf=1 E= (+ + 1) = K (1-) on [E = 0.75k) - ☺ = 3 * = 0-75k case- - If ni= 3, nf = 1 E= *(+-) = k = 0.89 on [E= 0.89 kr - 4

Case - If ni= 5 and nf = 4 E = K[nra ne ae = * [to - 1125] E = KM SXTO - og det = 0.0225K or TE = 010225 – ☺ case - - If ni= 4 and nf = 2 Ez* [-to J =* (**) = on [E = 0.19 K –©

case-③ If ni= 6 and nf=4 Then E= * [to #] =* (3546) on E= 20% = 0.035k on TE = 0.035k - since, energies 0.0225k and 0.035k are less than the 0.071k. So, the corect options are as follows:- © n=5 to n=4 and @ n=6 to n=4.