# Critical temperature of a superconductor

• viviane363
In summary, the critical temperature of a superconductor, TC, is related to the isotopic mass, M, by the equation TC * square root(M) = a constant. For lead, with an isotopic molar mass of 207.7 g, TC = 7.184 K. To find the critical temperature for an isotopic molar mass of 136.3 g, the same equation can be used and solved for TC. After correcting a possible algebraic error, the correct answer is 8.868 K. This aligns with the understanding that as the mass decreases, the critical temperature should increase.

#### viviane363

I have this problem here that I don't understand:
The critical temperature of a superconductor, TC varies with the isotopic mass of the element making up the superconductor, M, according to the relation TC *square root(M) = a constant. In lead, TC = 7.184 K for the isotopic molar mass 207.7 g. What is the critical temperature for the isotopic molar mass 136.3 g?

What I did since TC *square root(M) = a constant, I wrote the same formula for the temp we are looking for and said that both equality are equal since a is constant, and then solve for TC(the one we are looking for), but the answer doesn't seem right.
Can you tell me what I am supposed to do? thanks

Sounds like you're on the right track. What answer did you get?

I got 5.8196 K but it doesn't seem to be the right answer

You are right, since if the mass goes down then the TC should go up in order to compensate.

How did you set up the problem? (In mathematical terms so I can see where you went wrong)

I would guess it's a simple algebraic error.

i pose TC1*square root(M1)= a = TC2*square root(M2) oh! i might have made a mistake of rearranging and solving.now i got 8.868 K

Yea, that's what I got too.

Thank you very much