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

1 that is 100%

Step-by-step 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=
`(1)/(2)* \varepsilon_0* E^(2)`

E=
`(1)/(2)* 8.854* 10^(-12)* \left ( 10^(9) \right )^2`

E=
`4.427* 10^(6)joule`

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

E=
`2.76* 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