Which one has the largest energy gap between two energy...

Which one has the largest energy gap between two energy levels with the principal quantum numbers (n) as indicated in the H atom? n = 3 and n = 5 n = 5 and n = 8 n = 2 and n = 3 n = 1 and n = 2

Transcript

00:01 Okay, we need to answer what transition in a hydrant atom requires the largest change in energy.

00:05 We'll recall that the energy, the change in energy, is proportional to 1 over n1 squared minus 1 over n2 squared, right? so whatever the largest difference in n1's 1 over n1 squared and 1 over n2 squared is is going to be our answer, right? so let's go through these options.

00:32 We've got n1 equals 2, so that's 1 over 4.

00:36 And n2 equals 4, so minus 1 over 16.

00:42 B, we've got n1 equals 1, so 1 over 1, minus n2 equals 3, so that's 1 over 9.

00:53 For c, we've got n1 equals 1, so that's 1 over 1, minus n2 equals 2, so that's 1 over 4.

01:03 And d, we've got n1 equals 9, 1 over 9 squared.

01:08 So that's actually 1 over 81 minus n2 equals 10.

01:16 So that's 1 over 100.

01:19 And we do have an e as well.

01:21 So e is n1 equals 2, so that's 1 over 4.

01:25 And n2 equals 3, so that's 1 over 9.

01:31 So really, if we just compute these, we can just pick the largest.

01:39 I can say there's kind of an obvious one that's going to be the largest, right? this is one minus one -ninth.

01:49 This is eight -ninth.

01:52 That's nearly close to one.

01:55 The largest you could possibly get would be one over one over infinity, which would represent the dissociation entirely of an atom after having been in the n -equals -one shell.

02:10 So this would effectively just be one.

02:12 And this is the largest transition you can get...

Question

Which one has the largest energy gap between two energy levels with the principal quantum numbers (n) as indicated in the H atom? n = 3 and n = 5 n = 5 and n = 8 n = 2 and n = 3 n = 1 and n = 2

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