Bohr Model

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MedPR

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Which statements are valid regarding the energy level in a bohr model?

I. As the value of n increases, the electron is farther from the nucleus, therefore the electron is in a higher energy state.

II. As the value of n increases, the difference between adjacent energy levels (with n values differing by one), gets smaller.

III. A larger nuclear charge has no effect on transition energies, although it lowers all of the energy levels.

A. I only
B. I and II


Answer is: B

The image given in the book is

bohr-model.jpg


It very clearly shows that the energy levels spread out as the numbers increase (e.g 2 is closer to 1 than 3 is to 2). TBR explanation actually disputes this and says that 3 is closer to 2 than 2 is to 1.

So how is II true?

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bad image. 1-2 have the greatest energy gap, 2-3 have a smaller energy gap, et cetera.

i can't prove it to you because i don't remember the details and formulas, but i'm very certain that the above is accurate.
 
bad image. 1-2 have the greatest energy gap, 2-3 have a smaller energy gap, et cetera.

i can't prove it to you because i don't remember the details and formulas, but i'm very certain that the above is accurate.

It sucks because the image TBR refers to (passage 3, gen chem chapter 2) is very similar to the one I have posted. It shows that 3 and 4 are further apart than 1 and 2.

Why do the gaps get smaller and smaller?
 
It sucks because the image TBR refers to (passage 3, gen chem chapter 2) is very similar to the one I have posted. It shows that 3 and 4 are further apart than 1 and 2.

Why do the gaps get smaller and smaller?

The intuition is actually quite simple. I like the think of the electrons as planets orbiting a star (the nucleus). Planets that are closer to the star are going to be strongly affected by the star's gravity, which causes them to have tighter orbitals than planets farther from the star. Now taking this analogy to the atomic level, as the electrons get farther from the positively charged nucleus their attraction to it decreases, hence there are "bigger gaps" between orbitals. The electrons near the nucleous are the most strongly attracted and are extremely hard to remove. However, the electrons in the outter-most shell (valence electrons) are very loosely bound to the nucleus and require significantly less energy to remove than those that are closer to the nucleous.
solarsystem-800.jpg
 
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That's exactually what TBR is saying. 3-2 is farther away than 2-1, so it is closer in energy levels. as you get farther away from the nucleus and n increases, the Zeff becomes less important so the energy levels arent as far apart ya dig?
 
It sucks because the image TBR refers to (passage 3, gen chem chapter 2) is very similar to the one I have posted. It shows that 3 and 4 are further apart than 1 and 2.

Why do the gaps get smaller and smaller?

I don't think we need to memorize this but, according to Kaplan, "the difference in energy between two shells decreases as the distance from the nucleus increases because the energy difference is a function of [1/n^2i - 1/n^2f]"
 
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