Chapter 6: Q21E (page 224)

What fraction of a beam of $50 e V$ electrons would get through a $200 V 1 n m$ wide electrostatic barrier?

Short Answer

Expert verified

The required answer is $1.1 \times 10^{- 54}$

Step by step solution

Definition of Tunneling

Tunneling defines the penetration of a barrier of high energy by a low-energy wave or particle. For a wide barrier that transmits ineffectively:

$T = 16 \frac{E}{U} (1 - \frac{E}{U}) e^{- 2 k l}$

Where, $k = \frac{\sqrt{2 m (U - E)}}{}$ and l is width of penetration barrier, $U = q V$

Given/known parameters

$V = 200 V, E = 50 e V, I = 1 n m = 10^{- 9} m$

Solution

$U = q v = \frac{1.6 \times 10^{- 19} \times 200 J}{1.6 \times 10^{- 19} e V / J} = 200 e V$

$k = \frac{\sqrt{2 \times 9.1 \times 10^{- 31} \times (200 - 50) \times 1.6 \times 10^{- 19} J / e V}}{1.05 \times 10^{- 34}}$

$k = 62.7 \times 10^{9} m^{- 1}$

Now, $T = 16 (\frac{50}{200}) (1 - \frac{50}{200}) e^{- 2 \times 62.7 \times 10^{9} \times 10^{- 9}} = 1.1 \times 10^{- 54}$

Explanation and Conclusion

The fraction of beam of $50 e V$ transmitted through a barrier of $200 V$ and $1 n m$ width is $1.1 \times 10^{- 54}$ .

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What fraction of a beam of $50 e V$ electrons would get through a $200 V 1 n m$ wide electrostatic barrier?

Short Answer

Step by step solution

Definition of Tunneling

Given/known parameters

Solution

Explanation and Conclusion

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What fraction of a beam of 50eVelectrons would get through a 200V1nm wide electrostatic barrier?

Short Answer

Step by step solution

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Given/known parameters

Solution

Explanation and Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

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What fraction of a beam of $50 e V$ electrons would get through a $200 V 1 n m$ wide electrostatic barrier?