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Chapter 40, Problem 33AP

(a)

To determine

Transmission probability for quantum mechanical tunnelling of electron.

(b)

To determine

Transmission probability for quantum mechanical tunnelling of electron with energy deficit of 1.00eV.

(c)

To determine

Transmission probability for quantum mechanical tunnelling of alpha particle with energy deficit of 1.00MeV.

(d)

To determine

Transmission probability for quantum mechanical tunnelling of a bowling ball with energy deficit of 1.00J.

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Calculate the transmission probability for quantum-mechanical tunneling in each of the following cases. (a) An electron with an energy deficit of U - E= 0.010 0 eV is incident on a square barrier of width L = 0.100 nm. (b) An electron with an energy deficit of 1.00 eV is incident on the same barrier. (c) An alpha particle (mass 6.64 × 10-27 kg) with an energy deficit of 1.00 MeV is incident on a square barrier of width 1.00 fm. (d) An 8.00-kg bowling ball withan energy deficit of 1.00 J is incident on a square barrier of width 2.00 cm.
Quantum mechanical tunnelling enables chemical reactions to proceed that would be energetically impossible in classical mechanics. Assume that hydrogen (H) and tritium (T) atoms, each with a kinetic energy of 0.9 eV, encounter a potential barrier that is 1.0 eV high and 100 pm broad. Calculate the ratio of probabilities for transmission of the H and T atoms through the barrier. Note: the masses of H and T atoms are 1.674 x 10-27 kg and 5.008 x 10-27 kg, respectively, and 1 eV=1.602x10-19 J.
In a simple model for a radioactive nucleus, an alpha particle                            (m = 6.64 * 10-27 kg) is trapped by a square barrier that has width 2.0 fm and height 30.0 MeV. (a) What is the tunneling probability when the alpha particle encounters the barrier if its kinetic energy is 1.0 MeV below the top of the barrier (Fig. )? (b) What is the tunneling probability if the energy of the alpha particle is 10.0 MeV below the top of the barrier?
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