Why Do X-Ray Spectra Involve Inner Electron Shells?

[AznBoi]

I have a few practice test questions that I have gotten wrong and would like to know why. (I have the answers, but not the explanations)

1. Quantum transitions that result in the characteristic sharp lines of the X ray spectrum always involve
a. the inner electron shells
b. electron energy levels that have the same principal quantum number
c. emission of beta particles from the nucleus
d. neutrons within the nucleus
e. protons within the nucleus

I put (b) for this answer because I thought the energy levels were related to the wavelength of the absorbed/emitted photons and spectrums depend on wavelength of radiation? Correct answer is (A)

2. Quantities that are conserved in all nuclear reactions include which of the following?
I. Electric charge
II. Number of nuclei
III. Number of protons

a. I only b. II only c. I and III only
d. II and III only e. I, II, and III

I picked (C) because I thought that both charge and protons (the atomic number Z) need to be conserved and must be equal on both sides of the reaction equation. Can someone please give me an explanation of why charge is conserved (I just heard it somewhere) and # of protons are not?

 

[Hootenanny]

I have a few practice test questions that I have gotten wrong and would like to know why. (I have the answers, but not the explanations)

1. Quantum transitions that result in the characteristic sharp lines of the X ray spectrum always involve
a. the inner electron shells
b. electron energy levels that have the same principal quantum number
c. emission of beta particles from the nucleus
d. neutrons within the nucleus
e. protons within the nucleus

I put (b) for this answer because I thought the energy levels were related to the wavelength of the absorbed/emitted photons and spectrums depend on wavelength of radiation? Correct answer is (A)

Indeed, the wavelengths of the spectral lines do depend on the radiation wavelength. Consider the typical energy of an x-ray photon (10nm-0.01nm), now consider the difference in energy levels between the lower shells (n=1, n=2 etc). Do these energy levels get close together, or futher apart as n increases?

2. Quantities that are conserved in all nuclear reactions include which of the following?
I. Electric charge
II. Number of nuclei
III. Number of protons

a. I only b. II only c. I and III only
d. II and III only e. I, II, and III

I picked (C) because I thought that both charge and protons (the atomic number Z) need to be conserved and must be equal on both sides of the reaction equation. Can someone please give me an explanation of why charge is conserved (I just heard it somewhere) and # of protons are not?

Consider $\beta$ decay.

 

[AznBoi]

Indeed, the wavelengths of the spectral lines do depend on the radiation wavelength. Consider the typical energy of an x-ray photon (10nm-0.01nm), now consider the difference in energy levels between the lower shells (n=1, n=2 etc). Do these energy levels get close together, or futher apart as n increases?

Consider $\beta$ decay.

Don't the energy levels get closer together as n increases? I'm just using the energy level equation: $$E_{n}=\frac{Z^_{2}}{n^{2}}E{1}$$

By the way, is E_1 always equal to -13.6V for any electron in any atom? I just need to know this ground level energy because only electrons move up and down energy level orbits right?

 

[Astronuc]

By the way, is E_1 always equal to -13.6V for any electron in any atom?

No. Only for the hydrogen atom. E₁ increases with Z.

The first ionization energy for He is 24.6 eV.

Ionziation energies of the outermost electrons or rather atoms/elements (which unfortunately are given in (kJ/mol).
http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/ionize.html

See - http://www.webelements.com/webelements/properties/text/image-line/e-binding-energy-k.html
http://www.webelements.com/webelements/properties/media/tables/line/e-binding-energy-k.gif

Somewhere there is an on-line resource with K and L series energies.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html

 

[AznBoi]

No. Only for the hydrogen atom. E₁ increases with Z.

The first ionization energy for He is 24.6 eV.

Ionziation energies of the outermost electrons or rather atoms/elements (which unfortunately are given in (kJ/mol).
http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/ionize.html

See - http://www.webelements.com/webelements/properties/text/image-line/e-binding-energy-k.html
http://www.webelements.com/webelements/properties/media/tables/line/e-binding-energy-k.gif

Somewhere there is an on-line resource with K and L series energies.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html

So if you have a different atom with a different number of protons then you'd have to find E_1 first by using $$E_{1}=Z^{2}E_{1}$$ right? How would you solve for E_{1} if there E_1's on both sides of the equation? What do you substitute for the E_1 on the right side of the equation?

 

[Hootenanny]

AznBoi, what I was getting at is x-ray photons have a relatively short wavelength and are therefore very energetic. This means that xray photons are only absorbed/emitted by electrons which undergo large energy level transitions. Since, as you correctly say the difference between the energy levels decreases as $n\to\infty$, xray photons are only absorbed/emitted by electrons at the lower energy levels (since $\Delta E$ is greatest here).

Does that make sense?