July 03, 2020, 06:49:16 AM
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Topic: Would effective nuclear charge play a role in e-'s jumping quantum orbitals?  (Read 3762 times)

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Offline Aqueous Maqueous

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Would effective nuclear charge play a role in an electron's ability to change its quantum level? I had my Chemistry midterm today. There was a question that asked: Describe the bohr model similarities between H and Br3+. Also, are they similar in their spectra emission?

I answered yes with the reason that Br will have exactly one electron left over and both atoms will have the electron in the n=0 orbital. I also said that the electrons will need the same amount of electromagnetic radiation to change states. That both atoms would emit the same wavelength of photon because they both have 1 electron in the same quantum level. As a result, because the energy given off is the same, they'll both show the same color on the line spectra.

Now the part that's bugging me; even though both atoms have 1 valence electron, would Bromine's 3 protons have affected it's ability to change quantum state? To be more specific, would the 3 protons, with it's effective nuclear charge as +3 as apposed to +2, require for the electromagnetic radiation to be larger in order for it to change quantum level? Or does the effective nuclear charge not play a role in how much EM radiation is needed to change the quantum level?

I briefly glanced the text book, and the internet but couldn't find a solution.

Offline Yggdrasil

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Consider this simplified case of an electron moving father away from the nucleus.  Will it take more energy to move an electron away from a beryllium (I assume you mean Be3+ not Br3+) nucleus or a hydrogen nucleus (hint: consider Coulomb's law)?

Offline Aqueous Maqueous

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Yes.  :(

Offline renge ishyo

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I wouldn't be too upset; you caught your own mistake before you got your test back! That means you are thinking which is the whole point of all of this. You'll most likely get partial credit for the explanation that Be3+ has one electron left over just like hydrogen so it's spectra can still be calculated using the Bohr model (the Bohr model only holds well for one electron "hydrogenlike" systems). But yeah, the energy levels will be different due to the stronger pull of the Be3+ nucleus. You can actually find the energy levels (approximately) for one electron systems with different atomic number (Z) using the equations from the Bohr model. For instance:

En = - Z2(R)/ n2

where R equals the rydberg constant, n equals the quantum level (with the minimum at n=1 in the bohr model; it is n=0 for the lowest level in wave mechanics), and Z as the atomic number for the chemical species you are considering.

So for hydrogen "Z" would equal 1 while for Beryllium "Z" would equal 4 in the above equation.

Offline Yggdrasil

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Yes.  :(

It is far better to know why you got a question wrong, than to know you've gotten a question right.

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