Question

Let's consider tunneling of an electron outside of a potential well. The formula for the transmission coefficient is Te-2L, where L is the width of the barrier and C is a term that includes the particle energy and barrier height. For a particular situation, if C 1.0 nm-1, and you find the tunneling coefficient is T-0.010 (1 % of the electron tunnels through the barrier), then what is the width of the barrier L? e-2CL, where Select the correct answer 1 of 3 attempts used

a.1.0 nm
b. 1.2 nm
c. 2.3 pm
d. 4.6 nm
e. 2.3 nm

Answer 1

Answer:

The width of the barrier is 2.3 nm

(e) is correct option

Explanation:

Given that,

Transmission coefficient is

$T=e^{-2cL}$

Tunneling coefficient T=0.010

$C = 1.0 n/m$

We need to calculate the width of the barrier

Using equation of transmission coefficient

$T=e^{-2cL}$

$L=\dfrac{ln(T)}{-2c}$

Put the value into the formula

$L=\dfrac{ln(0.010)}{-2\times10^{9}}$

$L=\dfrac{-4.60}{-2}\times10^{-9}$

$L=2.3\times10^{-9}\ m$

$L=2.3\ nm$

Hence, The width of the barrier is 2.3 nm