General Physics, 2nd Edition
General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
Question
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Chapter 28, Problem 37E

(a)

To determine

The energy difference between n=1 and n=2 states if the length of the box is 3fm.

(a)

Expert Solution
Check Mark

Answer to Problem 37E

The energy difference is 68.4MeV.

Explanation of Solution

Write the expression for the energy of the nth state of a particle confined in a box.

    En=n2h28ma2        (I)

Here, En is the energy in the nth state, h is Planck’s constant, m is the mass of the particle and a is the dimension of the box.

Conclusion:

Substitute 2 for n, 6.626×1034Js for h, 1.67×1027kg for m and 3fm for a in equation (I).

    E2=22(6.626×1034Js)28(1.67×1027kg)(3fm)2(1fm)2(1015m)2=1.46×1011J(1eV1.6×1019J)=9.12×107eV=91.2MeV

Substitute 1 for n, 6.626×1034Js for h, 1.67×1027kg for m and 3fm for a in expression (I).

  E1=12(6.626×1034Js)28(1.67×1027kg)(3fm)2(1fm)2(1015m)2=3.65×1012J(1eV1.6×1019J)=2.28×107eV=22.8MeV

Evaluate the difference between E2 and E1.

    E2E1=(91.222.8)MeV=68.4MeV

Thus, the energy difference is 68.4MeV.

(b)

To determine

The energy difference between n=1 and n=2 states if the length of the box is 8fm.

(b)

Expert Solution
Check Mark

Answer to Problem 37E

The energy difference is 9.59MeV.

Explanation of Solution

Write the expression for the energy of the nth state of a particle confined in a box.

    En=n2h28ma2

Here, En is the energy in the nth state, h is Planck’s constant, m is the mass of the particle and a is the dimension of the box.

Conclusion:

Substitute 2 for n, 6.626×1034Js for h, 1.67×1027kg for m and 8fm for a in expression (I).

    E2=22(6.626×1034Js)28(1.67×1027kg)(8fm)2(1fm)2(1015m)2=2.05×1012J(1eV1.6×1019J)=1.28×107eV=12.8MeV

Substitute 1 for n, 6.626×1034Js for h, 1.67×1027kg for m and 8fm for a in expression (I).

  E1=12(6.626×1034Js)28(1.67×1027kg)(8fm)2(1fm)2(1015m)2=5.13×1013J(1eV1.6×1019J)=3.21×106eV=3.21MeV

Evaluate the difference between E2 and E1.

    E2E1=(12.83.21)MeV=9.59MeV

Thus, the energy difference is 9.59MeV.

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