Question

FAN AND MEDAL
1. In which of the following cases is the wavelength of the emitted radiation greatest?


Electron jumps from third orbit to second orbit.

Electron jumps from third orbit to first orbit.

Electron jumps from fourth orbit to first orbit.

Electron jumps from fifth orbit to second orbit.

Answer 1

when electron makes a transition, between state with energy Ei to another state with energy Ef, the frequency \nu of the emitted or absorbed photon is:
\[\Large h\nu = Ef - Ei\]

Answer 2

more precisely:
\[\Large h\nu = \left| {Ef - Ei} \right|\]

Answer 3

since we have considered the case of absorption of a photon

Answer 4

now we have:
\[\Large \nu = \frac{c}{\lambda }\]
so we can write:
\[\Large \frac{{hc}}{\lambda } = \left| {Ef - Ei} \right|\]
or:
\[\Large \lambda = \frac{{hc}}{{\left| {Ef - Ei} \right|}}\]

Answer 5

now the greatest wavelength corresponds to the smallest energy change

Answer 6

and the smallest energy change, happens when electron jumps the smallest number of levels

Answer 7

Electron jumps from fourth orbit to first orbit.

Answer 8

no, since the electron makes three transitions

Answer 9

I think when electron makes only one transition, do you see that option?

Answer 10

for example in the first option the electron goes from the third level to the second one

Answer 11

Whats the answer

Answer 12

so it makes only one transition, right?

Answer 13

yeah

Answer 14

therefore it is the first option