Answer :
Answer:
The tunnel probability for 0.5 nm and 1.00 nm are [tex]5.45\times10^{-4}[/tex] and [tex]7.74\times10^{-8}[/tex] respectively.
Explanation:
Given that,
Energy E = 2 eV
Barrier V₀= 5.0 eV
Width = 1.00 nm
We need to calculate the value of [tex]\beta[/tex]
Using formula of [tex]\beta[/tex]
[tex]\beta=\sqrt{\dfrac{2m}{\dfrac{h}{2\pi}}(v_{0}-E)}[/tex]
Put the value into the formula
[tex]\beta = \sqrt{\dfrac{2\times9.1\times10^{-31}}{(1.055\times10^{-34})^2}(5.0-2)\times1.6\times10^{-19}}[/tex]
[tex]\beta=8.86\times10^{9}[/tex]
(a). We need to calculate the tunnel probability for width 0.5 nm
Using formula of tunnel barrier
[tex]T=\dfrac{16E(V_{0}-E)}{V_{0}^2}e^{-2\beta a}[/tex]
Put the value into the formula
[tex]T=\dfrac{16\times 2(5.0-2.0)}{5.0^2}e^{-2\times8.86\times10^{9}\times0.5\times10^{-9}}[/tex]
[tex]T=5.45\times10^{-4}[/tex]
(b). We need to calculate the tunnel probability for width 1.00 nm
[tex]T=\dfrac{16\times 2(5.0-2.0)}{5.0^2}e^{-2\times8.86\times10^{9}\times1.00\times10^{-9}}[/tex]
[tex]T=7.74\times10^{-8}[/tex]
Hence, The tunnel probability for 0.5 nm and 1.00 nm are [tex]5.45\times10^{-4}[/tex] and [tex]7.74\times10^{-8}[/tex] respectively.