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Chapter 7: Q85CE (page 285)

The expectation value of the electron’s kinetic energy in the hydrogen ground state equals the magnitude of the total energy (see Exercise 60). What must be the width of a cubic finite wall, in terms of a0, for this ground state to have this same energy?

Short Answer

Expert verified

The width of the cubic finite wall should be 0.29 nm, about five times the Bohr radii.

Step by step solution

01

A concept:

Energy of the cubic finite wall can be given by,

E1,1,1=3π2h22mL2

Where, his Planck’s constant, Lis the width of the wall, and mis the mass.

02

Width of the cubic finite wall:

Rewrite the equation for energy as below.
13.6eV=3π2h22mL2L=πh32m×13.6eV=3.14(1.055×10-34J.s)2(9.11×10-31kg(13.6×1.6×1019J)/3=0.29nm

Hence, width of the wall is 0.29 nm .

03

Width in terms of a0:

As you know that,a0=0.05nm

Where,a0 is the radius of the hydrogen atom.

Hence, the obtained width of the wall is about five times that of the a0.

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