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

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Homework Help Overview

The discussion revolves around calculating the donor-electron ionization energy of a silicon crystal, utilizing given parameters such as electron effective mass and dielectric constant. The original poster presents a formula and their computed result, which they question for accuracy.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of a specific formula for ionization energy, with the original poster detailing their calculations and values used. Questions arise regarding potential calculation errors and the correctness of the input values.

Discussion Status

There is an ongoing examination of the calculations presented, with participants providing feedback on the plausibility of the results. Some participants suggest re-evaluating the calculations and checking for errors in the input values, indicating a collaborative effort to clarify the problem.

Contextual Notes

Participants are working under the constraints of the problem statement, which includes specific values for effective mass and dielectric constant, and are focused on ensuring the accuracy of their calculations without reaching a definitive conclusion.

ee1215
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Homework Statement


Find donor-electron ionziation energy of silicon crystal. Electron effective mass mc=.98mo and dielectric constant ε/εo=12.3

Homework Equations


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


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?
 
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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
 
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.
 
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
 
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?
 
ee1215 said:
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!:smile:If you feel the result impossible try to estimate its magnitude without calculator.

ehild
 

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