# Homework Help: Energy of Donor Electron

1. Oct 7, 2011

### ee1215

1. The problem statement, all variables and given/known data
Find donor-electron ionziation energy of silicon crystal. Electron effective mass mc=.98mo and dielectric constant ε/εo=12.3

2. Relevant equations
I use the ED=-(1/4πε)2*[(mc*e4) / (2*(h/2π)2)]

3. The attempt at a solution
My answer of -1.415x10-54 does not seem right. I solved for mc and ε from given equations in the problem and plugged in. Is this correct or have I made a mistake?

2. Oct 7, 2011

### ehild

What you did is correct in principle. You could made same calculation error or plugged in wrong value for m0. Show your data and calculation. And what unit of energy did you use?

ehild

3. Oct 8, 2011

### ee1215

Well, using the ED formula mentioned above. I solved for mc = .98*9.1094x10-31 = 8.927x10-31kg and solved for ε=12.3*8.854x10-12 = 1.089x10-10F/m. Plugged those two equations into ED, and also h-bar = 1.054x10-34Js and e=1.6022x10-19C, I got the answer I mentioned above in my calculation.

4. Oct 8, 2011

### ehild

Your result is impossible. Count the exponents: 4*(-19)+(-31)-(2*(-12)+2*-(34)). It is -15. Multiply the numbers, this gives a magnitude of 10-5. So the result is of magnitude 10-20Joule.

ehild

5. Oct 8, 2011

### ee1215

You are correct. Even though I thought I double checked me answer before I posted the question, I just did the calculation and got -1.4138x10-20. This is more reasonable?

6. Oct 8, 2011

### ehild

Sure!If you feel the result impossible try to estimate its magnitude without calculator.

ehild