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Problem 43 Hard Difficulty

A bismuth target is struck by electrons, and x-rays are emitted. Estimate (a) the M-to L-shell transitional energy for bismuth and (b) the wavelength of the x-ray emitted when an electron falls from the M shell to the L shell.

Answer

a) 14000 $\mathrm{eV}$
b) 0.089 $\mathrm{nm}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Farnaz M.

Other Schools

Meghan M.

McMaster University

Video Transcript

in question. A have to estimate the transitional energy from the M shell to the L shell for the bismuth that has an atomic number off 83. So we can estimate we can estimate the energy off the 10th level off the bismuth. We can make an approximation s minus the effective. That's on atomic number square times 13.6 and a vote divided by and squared where the effective atomic number is the atomic number Z minus the number off electrons. That shield I'm gonna call that. Just be the number of, like, electrons that shield the shell that very interested in, um, from the nucleus. Okay, so in our case, we have to calculate the energies of the end. The show em in the show. L Well, uh, show em corresponds, shoot and equals three. So we're gonna Kakheti three. That's gonna be minus the effective ah, atomic numbers. Where on the effect effective atomic number in this case is Z, which is 83 minus the number off elections that shoud the shell n equals three from the nucleus and notice that there are two electrons in the K shell in the first energy level. And there are seven, uh, set seven electrons in the L Shell in the second energy level. They because, ah, the the L shell is a complete. And that's why the the election is able to transition from the M shell to the L show. Okay, so in total, there are nine electrons shooting the M shell from the nucleus. So this is the 80 83. Minus nine is the effective atomic number times 13.6 votes divided by and square, which is nine. So this is just equal to minus eight point 27 kilo electoral votes. And this is the energy of the M show I'm gonna highlighted in blue. And now we can calculate the energy for the L show. So the energy for the second energy level is minus 83 minus the number of electrons that are shooting the the L Shell. And in this case, there are only two electrons in the K shell that are shooting the L shell. So this is minus two square times 13.6 electoral votes divided by foursquare. I'm started to square just four. So this is minus 22 0.3 killer electoral votes. This is the energy of the L show. And what we want is to calculate the transitional energy. So really, what we want is Delta that's equal to end to e m minus e l. So e. M is mine is 8.27 killer Like some votes, yell is 22.3 killer from votes. So without a is equal to 14 2003 killer like from votes. Okay, this is a transitional energy between the M in the l Shell. Four questions be You have to come early. What is the wavelength of the photon that's emitted in the process of transitioning from the M to the L shells? Well, in that case, you know that the energy off the immediate Fulton would be just the transitional energy between the two levels and this is equal to H C over London. That's the energy of the photo. So Lunda is equal to H C over doubt. E HC is 1240 electoral votes in the meters and that a is 14.3 time stood to the third electron vote, So Lunder is equal to 8.85 times sent to the minus two millimeters, which is the same as 88.5 B commuters. This is the wailing

Universidade de Sao Paulo
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Farnaz M.

Other Schools

Meghan M.

McMaster University