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Problem 45 Hard Difficulty

The $\mathrm{K}$ series of the discrete spectrum of tungsten contains wavelengths of $0.0185 \mathrm{nm}, 0.0209 \mathrm{nm},$ and 0.0215 $\mathrm{nm}$ . The K-shell ionization energy is 69.5 $\mathrm{keV}$ . Determine the ionization energies of the $\mathrm{L}, \mathrm{M},$ and $\mathrm{N}$ shells.

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Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Jared E.

University of Winnipeg

Meghan M.

McMaster University

Video Transcript

In this exercise, we have three wavelengths that belong to the K series of the tungsten. So we have the wavelength from the one equals 2010185 centimeters. London to equals to 0.2 09 centimeters. Well, under three equals to 0.2 15 millimeters. Ah, and we also have the information that the ionization energy for the K series Ah, the K shell off the tension which under called a E k i for ionization is equal to 60 9.5 killer like from goats. So notice that if the energy required to lionize the K series I'm sorry, the K ah shell is 69.5 killer electoral votes that the energy of the K shell itself is minus 69.5 Killer from votes. Okay. Ah, and we have to calculate the energies. Ah, the organization energies of the else shell, the M shell and for the end show. Let me just write an a little better here, So and okay, we need to find these three ionization energies. Okay. Ah, how can we do it first? We have the wavelength of three. Fulton's that are emitted in belong to the K series of the tungsten. So we can find the energies of each one of these photons and then it confined from which shell the electron jumped. Ah Ah! And with that information, we can find what is the energy of that show? And that is enough to calculate the ionization energy of that shot. So first of all, I will calculate e one. Okay, He one is the energy of the first Fulton. So this is a judge. See Over Linda one. This is 240 electoral votes. Then the meters divided by Hello. I'm the one which is zero points you 185 millimeters. So the energy if 67 ah kill electoral votes. Yeah, the energy of a second Fulton is a C over London two. So this is 1240 electoral votes and meters divided by 0.0. Choose your nine millimeters so this is equal to 59.3 kill electoral votes. And finally, the energy of the third Fulton is equal to 12 under in 40 electoral votes. Centimeters. If I did by 0.0 to 15 millimeters and this is 57.7 kill electoral votes. Okay, so these are the energies of the fortunes, Uh, noticed that the large the smallest energy corresponds to the transition from the smallest shell the smallest, uh, the smallest energy level to the K level. So we have basically is four energy levels here, okay? And I'm gonna label them have the K. That's the lowest. Then we have the L than the M than the end. I noticed that the energy required to go from the L A to the K uh, Shell is smaller than the energy required to go from the M to decay. And that is smaller than the energy required to go from the end to the case. So we know that the smallest energy among those we calculated here come from the election transitioning from the L to the k ah shells. And the smallest energy is e three. So have at e three is equal to the energy of the L Shell. Milas. The energy of a K show. Okay, so you can isolate yell here, and e l is equal to e k plus the three, as we calculated before Ikea is minus 69.5 kilo electoral votes and e three is 57.7 killer electoral votes. So e l is equal to minors, 11.8 killer electoral votes. Okay, that's the energy off the of the L Shell. So this means that the ionizing energy is just minus yell. So the ionizing energy e l I is equal to 11 0.8 killer electric boats. Okay, then it can go to the ionizing energy off the M Shell. Uh, I'm sorry of the yeah of the m shell. That's right. That's gonna be the second smallest energy among the transition from the M shelf. Decay shall results in the second smallest energy for the folds. So that's E two equals 59.3. So have that he, too, is able to e m minus e k. So again, him is UK blessed to. So this is, uh okay, that that's minus minus 59 went five kilogram votes plus eat you and that's just 59.3 kill electoral votes. So we have that e m is able to minus 10 point to kill electing votes. And the ionizing interview for the M Shell is 10.2 Fullerton votes. And finally, the greatest fulton energy of corresponds to the transition from the and shell to the K. And that is 67 kill electoral votes. So we have that the energy e one evils you in minus E. K. So, yeah, he who's a K thus he won. And this is minus 69.5. As always, killer like from votes Plus you want. And that's 67 uh, kill election votes. Okay. And this is equal to So have a n equals two minus 2.5 killer electron books. So the ionizing interview for the end shell is 2.5 killer electron volts. Okay, so you have these three answers your for E I M e I am and e i l and our exercises complete.

Universidade de Sao Paulo
Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Jared E.

University of Winnipeg

Meghan M.

McMaster University