Question

18. Consider the potential barrier as shown in the figure. Calculate the transmission coefficcient. Discuss the depence of this coefficient. This is so called tunneling effect. Give a physical phenomenum that can be explained by this fact. E 00 0 V1 V(x) = x < 0 -V 0 < x <a V2 a< x <b 0 x <b

Answer 1

soln Video and @The given potential bameo is as follows, na bir donde E taustast on oth b Vi where the particle has energy E which is less than the potential barrier i.e. ELV. The potential for aco is to. Thus the particle is stuck between 0 and a. Classically, the particle would need total energy more than the potential barrier ₂ to become tree (i.e. to come out of the region between a fb). But quantum mechanically the particle can penetrate through the potential bassies and appear on the other side. The probability of tunneling lie transmission coefficient is given as -red where v - It² where P Probability of tunneling or transmission coefficient P= e 2m (vg E) d with of the barrier (distance between afb) m mass of the particle Thus, the transmission coefficient depends on the width of the barrier and the height of the barrier (ie. /2) so, the transmission coefficient will decrease if distance between afb increases and increases and vice versa.

The example of such effect is the Gamow's theory of a decay. According to this theory, the a particles are stuck inside the nucleus. These a particles have total energy less than the nucleus's potential barrier. But we do observe the & radiations due to the tunneling effect.