Einstein model of solids, energy in joules of one quantum

[Deadsion]

Homework Statement

the stiffness of the interatomic "spring" (chemical bond) between atoms in a block of lead is 5 N/m. Since in our model each atom is connected to two springs, each half the length of the interatomic bond, the effective "interatomic spring stiffness" for an oscillator is 4*5 N/m = 20 N/m. The mass of one mole of lead is 207 grams (0.207 kilograms).

What is the energy, in joules, of one quantum of energy for an atomic oscillator in a block of lead?

Homework Equations

E= hbar*sqrt(k/m)

The Attempt at a Solution

E=(1.05457148e-34)(sqrt(20/.207)
E=1.033e-33 J

After this i thought that i would just divide this number by the total number of oscillators and get the energy for one quanta, but that doesn't work. This is the only equation given in the book besides the one for finding the possible number of microstates, but i don't see how that would help.

 

[Redbelly98]

I think you're done. It asks for the quantum of energy for an (as in one) atomic oscillator, and that is what you did.

 

[Deadsion]

Oh I figured out why it was wrong, its supposed to be the mass of one atom, not one mole. so m = .207/6.02e23
E=hbar*sqrt(20/m)
E=8.0427e-22 J

 

[Redbelly98]

Aaargh, I missed that. Good catch.