Suppose a beam of 5.0 eV protons strikes a potential energy barrierof height 6.0

Question

Suppose a beam of 5.0 eV protons strikes a potential energy barrierof height 6.0 eV and thickness 0.56 nm, at a rate equivalent to a currentof 1080 A. (a) How long would you have to wait-on average-for one proton to betransmitted?
s

(b) How long would you have to wait if the beam consisted ofelectrons rather than protons?
s (a) How long would you have to wait-on average-for one proton to betransmitted?
s

(b) How long would you have to wait if the beam consisted ofelectrons rather than protons?
s

Explanation / Answer

U = 6.0 eV = 9.6 x 10-27 J E = 5.0 eV = 8 x 10-27 J m = 1.673 x 10-27 kg for proton      = 9.1 x 10-31 kg forelectron h = 6.63 x 10-34 J-s L = 0.56 x 10-9 m q = 1.6 x 10-19 C I = 1080 A We know that           Transmissioncoefficient   T = e(-2bL) Where b = [82 m (U - E) /h2] Therefore time take for proton or electron to transmittedis       t = q / I* T                             Substitute values and solve for time 't'.

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