Question

Electrons will readily tunnel out of the surface of a metal when a sufficiently high electric field E is applied to the surface. Suppose that for a certain metal the fermi energy is 5.0 eV, and work function is 4.0 eV. Estimate the probability that an incident electron will tunnel out if E = 1 x 109 V/m .

Answer 1

Answer:

1 that is 100%

Explanation:

here it is given that Fermi energy of the of the metal = 5 e.V

work function= 4 e.V

we have to find the probability that an incident electron will tunnel out if E=109 V/m

WORK FUNCTION : work function is defined as the energy required to withdraw an electron completely from the metal surface.

now the energy per unit volume in electric field is given by

E= $\frac{1}{2}\times \varepsilon_0\times E^{2}$

E=$\frac{1}{2}\times 8.854\times 10^{-12}\times \left ( 10^{9} \right )^2$

E=$4.427\times 10^{6}joule$

in electron volt E=4.427\times 10^{6}joule × 6.24\times 10^{18}

E=$2.76\times 10^{25}e.V$

hence the applied energy per unit volume is greater than the work work function of electron so there is probability of 100% that electron will tunnel out