Question

Which of the following electron jumps in a hydrogen atom emits the photon of highest frequency?

a) n=2 to n=3
b) n=1 to n=2
3) n=3 to n=2
4) n=2 to n=1

Answer 1

The jump which emits the highest frequency will be the jump with the greatest energy, as energy is related to frequency as

where is Planck's constant. Analytically, the frequency can be found out by the following relation

where is the Rydberg's Constant, and is the speed of the light.

a) For the transition of

The negative sign implies that radiation is not emitted, but absorbed to facilitate this transition from a lower energy to a higher one.

b) For the transition of

The negative sign implies that radiation is not emitted, but absorbed to facilitate this transition from a lower energy to a higher one.

c) For the transition of

This transition emits a photon with a frequency equal to the numeric value of the above expression. I have not simplified it as its simpler to work with the constants.

d) For the transition of

We know that only Options C and D emit radiation, the other two requiring radiation to occur.

We also know that since , Option D has the highest frequency.

Option D is the correct answer.