What is the Donor-Electron Ionization Energy of Silicon Crystal?

[ee1215]

Homework Statement

Find donor-electron ionziation energy of silicon crystal. Electron effective mass m_c=.98m_o and dielectric constant ε/ε_o=12.3

Homework Equations

I use the E_D=-(1/4πε)²*[(m_c*e⁴) / (2*(h/2π)²)]

The Attempt at a Solution

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

 

[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

 

[ee1215]

Well, using the E_D formula mentioned above. I solved for m_c = .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 E_D, and also h-bar = 1.054x10^-34Js and e=1.6022x10^-19C, I got the answer I mentioned above in my calculation.

 

[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

 

[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?

 

[ehild]

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?

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

ehild