91影视

Equation for penetration distance=

$畏=\frac{\mathrm{鈩�}}{\sqrt{2m\left(U_0-E\right)}}$

Here,

$\mathrm{鈩�}$= reduced Planck's constant,

$m$= mass of the particle,

$U_0$=height of the potential barrier, and

$E=$energy of the incident particle.

Probability of tunneling through the potential barrier,

$P_{\text{tunnel}}=e^{-\frac{w}{畏}}$

Substituting $\frac{\mathrm{鈩�}}{\sqrt{2m\left(U_0-E\right)}}\text{=}畏$,

$P_{\text{tunnel}}=e^{\frac{2w}{\sqrt{2m\left(U_0-E\right)}}}$

$=e^{\frac{2\sqrt{2m\left(U_0-E\right)}}{\mathrm{鈩�}}w}$

$P_{\text{tunnel (a)}}=e^{\frac{2\sqrt{2m\left(U_0-E\right)}}{\mathrm{鈩�}}w}$

$P_{\text{tunnel (a)}}=e^{\frac{2\sqrt{2\left(9.11脳{10}^{-31}\mathrm{kg}\right)\left(1\mathrm{eV}\right)\left(\frac{1.60脳{10}^{-19}\mathrm{J}}{1\mathrm{cV}}\right)}\left({10}^{-9}\mathrm{m}\right)}{1.05脳{10}^{-34}\mathrm{Js}}}$

$=3.4165脳{10}^{-5}$

$P_{\text{tunnel (b)}}=e^{\frac{2\sqrt{2m\left(U_0-E\right)}}{h}w}$

$P_{\text{tunnel (b)}}=e^{\frac{2\sqrt{2\left(9.11脳{10}^{-31}\mathrm{kg}\right)\left(2\mathrm{eV}\right)\left(\frac{1.60脳{10}^{-19}\mathrm{J}}{1\mathrm{cV}}\right)}}{1.05脳{10}^{-34}\mathrm{J}\mathrm{s}}\left({10}^{-9}\mathrm{m}\right)}$

$=4.815脳{10}^{-7}$

$P_{\text{tunnel (c)}}=e^{\frac{2\sqrt{2m\left(U_0-E\right)}}{h}w}$

$P_{\text{tunnel (c)}}=e^{\frac{2\sqrt{2\left(9.11脳{10}^{-31}\mathrm{kg}\right)\left(1\mathrm{eV}\right)\left(\frac{1.60脳{10}^{-19}\mathrm{J}}{1\mathrm{cV}}\right)}}{1.05脳{10}^{-34}\mathrm{J}-\mathrm{s}}\left(2脳{10}^{-9}\mathrm{m}\right)}$

$=1.167脳{10}^{-9}$

$P_{\text{tunnel (d)}}=e^{\frac{2\sqrt{2m\left(U_0-E\right)}}{\mathrm{鈩�}}w}$

$P_{\text{tunnel (d)}}=e^{\frac{2\sqrt{2\left(9.11脳{10}^{-31}\mathrm{kg}\right)\left(2\mathrm{eV}\right)\left(\frac{1.60\mathrm{b}{10}^{-19}\mathrm{J}}{1\mathrm{eV}}\right)}}{1.05脳{10}^{-34}\mathrm{J}路\mathrm{s}}\left(0.5脳{10}^{-9}\mathrm{m}\right)}$

$=6.9465脳{10}^{-4}$

Thus, the rank of probabilities of tunneling through the barriers from largest to smallest,

$P_{\text{tunnel}\left(\mathrm{d}\right)}>P_{\text{tunnel (a)}}>P_{\text{tunnel}\left(\mathrm{b}\right)}>\text{and}{P}_{\text{tunnel}\left(\mathrm{c}\right)}$