Question

Free electrons that are initially at rest are accelerated in vacuum over a distance of 1.000 mm in a uniform electric field of 10.00kV/m and then strike a thin planar metal electrode, which acts like a square potential barrier. Averaged over a long time, exactly 1% of the electrons penetrate the metal and emerge on the other side. What is the thickness of the metal if the effective barrier energy Uo i s 11.6 electron-volts?

Answer 1

So the energy of free electron is given by,

d is distance and E is electric field

e is charge of electron so putting values we get,

energy of electrons as,

this is case of tunneling when E<V

and penetration depth is given by,

k is the wave vector associated to electron wave function

which is,

so putting values we get,

so penetration

or

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