Which electron transition in a hydrogen atom requires the largest amount of energy? a) 1-->2 b) 2-->3 c) infinity-->1 d) 3-->5?

When the energy of a photon is absorbed to promote an electron from n₁ to n₂.
Rydberg formula : 1/λ = R[(1/n₁²) - (1/n₂²)]
Also, energy of the photon : E = hc/λ

Then E = hcR[(1/n₁²) - (1/n₂²)], where
E : Energy required for an electron promotes from n₁ to n₂
h : Planck constant
c : Speed of light in vacuum
R = Rydberg constant

a) E = hcR[(1/1²) - (1/2²)] = 0.75hcR (The largest amount of energy required)
b) E = hcR[(1/2²) - (1/3²)] ≈ 0.14hcR
c) E = hcR[(1/∞²) - (1/1²)] = -hcR (Energy is released)
d) E = hcR[(1/3²) - (1/5²)] ≈ 0.071hcR

The answer : a) 1 → 2

There is no 'trick'. It requires some level of knowledge and understanding, but is easy when you have these.

First, I think this is a 'trick' question.

When the level number *increases* energy is required because the electron must be pulled away from the nucleus.

When the level number *decreases* energy is not required because the electron gives off energy when it 'falls'. No energy has to be supplied.

So answer c) is wrong because no energy is required. In fact energy is released (as a photon).

You need to know what the energy levels 'look' like. See link - look at the spacing between the lines and the numbers on the right.

You will see the gaps get smaller as n increases. The biggest gap is between n=1 and n=2. This gap is bigger than *all* the other gaps which don't start on n=1.

So answer a) is correct.

But if choice c) had said 1-->infinity, you should see from the diagram that it would be the correct choice.

An altenative is to work out the size of the gap. For a transmition from level n to level m the gap (energy change) is a constant times (1/n² - 1/m²) which you can work out. But that takes time/effort and isn't necessary for this particular question.