91影视

Given in the question

The energy of the photon beam $E=5.0\mathrm{eV}$

Height of the potential energy barrier$U_b=6.0\mathrm{eV}$

The thickness of the barrier $L=0.70\mathrm{nm}$

The striking current $l=1000A$

A particle for example electrons, or proton can reflect from any boundary at which its potential energy changes even when classically it would not reflect.

Classical physics states that if a particle's initial kinetic energy

exceeds the region's capacity for reflection, it should never do so.

However, there is a reflection by quantum physics.

The rate at which photon incident on the barrier can be given as

$n=\frac{l}{q}$

Where,$I$is the current and$q$is the charge.

role="math" localid="1663222277494" $\begin{array}{l}n=\frac{1000\mathrm{A}}{1.65脳{10}^{-19}\mathrm{C}}\\ n=6.25脳{10}^{-21}{\mathrm{s}}^{-1}\end{array}$

Therefore, waiting time can be given as

$t={\left(nT\right)}^{-1}$

Where, $T$is the transmission coefficient

The transmission coefficient of a particle can be given as.

$T=e^{-2bL}$

Where, $L$is the length of the potential barrier.

And $b$can be given as,

$b=\sqrt{\frac{8m^2\left(U_b-E\right)}{h^2}}$

Where the mass of the particle is $m$and $E$is incident energy and $U_b$is the height of the barrier

The transmission coefficient in the case of photon

role="math" localid="1663222263740" $T=exp\left[-2脳0.70脳{10}^{-9}\mathrm{m}\sqrt{\frac{8{\mathrm{蟺}}^2\left(1.6脳{10}^{-27}\mathrm{kg}\right)脳\left(6.0-5.0\right)\mathrm{eV}脳\left(1.602脳{10}^{-19}\mathrm{J}/\mathrm{eV}\right)}{{\left(6.626脳{10}^{-34}\mathrm{Js}\right)}^2}}\right]$

Therefore, the waiting time

role="math" localid="1663221743739" $\begin{array}{l}t={\left(nT\right)}^{-1}\\ =\frac{1}{n}{T}^{-1}\end{array}$

role="math" localid="1663222115467" $\begin{array}{rcl}t& =& \frac{1}{1.65脳{10}^{21}{\mathrm{s}}^{-1}}脳\exp \left[-2脳0.70脳{10}^{-9}\mathrm{m}\sqrt{\frac{8{\mathrm{蟺}}^2\left(1.6脳{10}^{-27}\mathrm{kg}\right)脳\left(6.0-5.0\right)\mathrm{eV}脳\left(1.602脳{10}^{-19}\mathrm{J}/\mathrm{eV}\right)}{{\left(6.626脳{10}^{-34}\mathrm{Js}\right)}^2}}\right]\\ & =& 3.37脳{10}^{111}\mathrm{s}\\ & =& {10}^{104}\mathrm{years}\end{array}$

The waiting time in case of a photon is ${10}^{104}\mathrm{years}$.

We know the formula for waiting time is

$\begin{array}{l}t={\left(nT\right)}^{-1}\\ =\frac{1}{n}{T}^{-1}\end{array}$

The transmission coefficient in the case of electron

$T=exp\left[-2脳0.70脳{10}^{-9}m\sqrt{\frac{8{\mathrm{蟺}}^2\left(9.11脳{10}^{-31}\mathrm{kg}\right)脳\left(6.0-5.0\right)\mathrm{eV}脳\left(1.602脳{10}^{-19}\mathrm{J}/\mathrm{eV}\right)}{{\left(6.626脳{10}^{-34}\mathrm{Js}\right)}^2}}\right]$

So, the waiting time,

$\begin{array}{rcl}t& =& \frac{1}{1.65脳{10}^{21}{\mathrm{s}}^{-1}}脳\exp \left[-2脳0.70脳{10}^{-9}\mathrm{m}\sqrt{\frac{8{\mathrm{蟺}}^2\left(9.11脳{10}^{-31}\mathrm{kg}\right)脳\left(6.0-5.0\right)\mathrm{eV}脳\left(1.602脳{10}^{-19}\mathrm{J}/\mathrm{eV}\right)}{{\left(6.626脳{10}^{-34}\mathrm{Js}\right)}^2}}\right]\\ & =& 2.1脳{10}^{-19}\mathrm{s}\\ & & \end{array}$Therefore, the waiting time in the case of the electron is $2.1脳{10}^{-19}\mathrm{s}$