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# The $\rho$ -meson has a charge of $-e,$ a spin quantum number of $1,$ and a mass 1507 times that of the electron. If the electrons in atoms were replaced by $\rho$ -mesons, list the possible sets of quantum numbers for $\rho$ -mesons in the 3$d$ subshell.

Atomic Physics

Nuclear Physics

### Discussion

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##### Andy C.

University of Michigan - Ann Arbor

##### Aspen F.

University of Sheffield

### Video Transcript

in this exercise, we have to consider the three d sub shell of an atom where the election has been replaced by a row maze. And we have to list all possible quantum numbers off the allowed quantum states for the three D sexual. The only thing that's gonna change here because of the presence of the row amazing is that the this been off the row? Mazen is one. While the spin of the electron it's minus is 1/2. So they allow spin numbers. M s for the row, Mazen here, minus one zero N one. Okay. Ah. And also noticed that an equals three that's the principal quantum number for the three DS of Show. And l equals two since the sub shell is de Okay, so d represents l equals two. And now I also noticed that because of the orbital quantum number being to the allowed values off ml, that is the magnetic quantum number ar minus two minus 10 one and two. Okay, so now we're in a position to list all possible quantum numbers in this of show. Okay, I'm gonna leave and equals three and our equals two implicit. Okay, because it's gonna pierre all throughout and exercise someone Every answer they assumed that n equals three and l equals two, and I can start listing. So in the 1st 1 and l, he was a minus two and s a close to minus one. The second m l equals two minus two a mess. It was zero in the third m l equals minus two m s. You will swan in the fourth. And now it was minus one. A mess equals minus one. In the fifth ML, it was minus one and M s Peoples zero the sixth and now equals minus one. M s equals one in the seventh and now equals zero and M s equals minus one. In the eighth ml, it will zero in a mess equals zero in the nine. And l equals zero and m s. It was plus one from the 10th and malleable zero. I'm sorry. Male. Um, Al equals Well, no m s equals minus one in the 11th. And now it was one. A mess equals zero in the 12. And now it was one a mess people spurs for in the 13th. Email equals two a mess. It was minus one the 14th and Mel, it was two and a mess because zero. And in the 15th m l equals two and m s equals. Let's one. So, um, this ends the exercise because we've listened all 50 impossible states for the three D show with the election substituted by a row mace.

#### Topics

Atomic Physics

Nuclear Physics

##### Andy C.

University of Michigan - Ann Arbor

##### Aspen F.

University of Sheffield