GREPhysics.NET: GR0177 #18

GR0177 #18

Problem

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Atomic $\Rightarrow$ }Bohr Theory

One can calculate the ionization energy from finding the ionization energy for He for He+, then subtracting it from the given ionization energy. Since He+ is a hydrogenic atom, one can apply Bohr Theory.

In Bohr Theory, the energy to remove an electron is $E=Z^2 E_1$ . For Helium, since it has two protons, $Z=2$ . Thus, $E=4 E_1 \approx 52$ is the ionization energy. ( $E_1=13.6eV$ is just 1 Rydberg or the energy of the ground state of Hydrogen.)

Subtract this from the ionization energy for He given in the problem to be 79 eV, to get an answer close to choice (A).

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Comments

star2009
2008-08-13 14:05:08

E = -13.6 Z^2/n^2rnrn Energy to keep a first electron, Z=2 and n=1 for heliumrnrnSo rn E = -13.6 * 2^2 = - 54.4 e V.rnrnTotal energy to keep both electrons= total energy to remove both electrons = 79 eVrnrnEnergy to keep First electron = Energy to remove last electronrnrnSo that rn Energy to remove first electron = 79-54.4 = 24.6 eVrnrnrnAccording to "Nature", the least binding electron has to be removed first. The weaker the earlier...........rnrnNature is not fair. It is suck!!!!rn

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KarstenChu
2007-03-22 13:52:41

I don't get this...in the second paragraph you state that E=Z^2E1 where Z=2 will be the ionization energy for Helium...so why do you have to subtract it from the energy require to remove both electrons to get the ionization energy for Helium? Don't you already have it? Respectfully, I do not believe this is the correct way to solve it and that carrie's rationale is closer to the mark.

kwooley
2007-09-27 20:47:44

KarstenChu - Though carrie's solution is a quick way to get the correct answer, I believe the original solution is correct. You are told how much energy is needed to remove both electrons. You can not apply the Bohr hydrogenic model to removing the first electron because He has two electrons. Thus you subtract the energy to remove the second atom from the total energy to get the energy it must have taken to remove the first electron.

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carrie
2005-12-09 14:26:18

It may also be useful to simply consider the fact that it will take more energy to remove the second electron than the first. Thus the energy to remove the first electron must be less than half the energy to remove both, and (A) is the only answer that it less than half of 79 eV.

Poop Loops
2008-10-31 22:18:24

Agreed. Calculating a number is the sucker's way of doing it.

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