Critical temperature of a superconductor

[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

 

[Matterwave]

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

 

[viviane363]

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

 

[Matterwave]

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.

 

[viviane363]

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

 

[Matterwave]

Yea, that's what I got too.

 

[viviane363]

Thank you very much