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Chapter 6: Q11E (page 1354)

Find the width L of a one-dimensional box for which the ground state energy of an electron in the box equals the absolute value of the ground state of a hydrogen atom.

Short Answer

Expert verified

The width L of a one-dimensional box is1.66脳10-10m for which the ground state energy of an electron in the box equals the absolute value of the ground state of a hydrogen atom.

Step by step solution

01

Define the energy level.

The energy level of a particle of mass in a box width is:

En=Pn22m=n2h28mL2=n2蟺2h22mL2n=1,2,3,...

02

Determine the width of box.

The energyE1 of hydrogen at ground level is 13.6 eV .

The energy E1in joule J is

E1=13.6脳1.60脳10-191=2.18脳10-18J

The mass of hydrogen is9.11脳10-31kg and value ofh=1.055脳10-34J.s .

The width of the box is:

L=n蟺丑2mEn=1蟺1.055脳10-3429.11脳10-312.81脳10-18=1.66脳10-10m

Hence, the width L of a one-dimensional box is1.66脳10-10m .

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