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Draw an energy level diagram for a. nonrelativistic
Chapter , Problem 14P(choose chapter or problem)
Problem 14P
Draw an energy level diagram for a. nonrelativistic particle confined inside a three-dimensional cube-shaped box, showing all states with energies below 15. (h2/8mL2 ) . Be sure to show each linearly independent state separately, to indicate the degeneracy of each energy level. Does the average number of states per unit energy increase or decrease as E increases?
Questions & Answers
QUESTION:
Problem 14P
Draw an energy level diagram for a. nonrelativistic particle confined inside a three-dimensional cube-shaped box, showing all states with energies below 15. (h2/8mL2 ) . Be sure to show each linearly independent state separately, to indicate the degeneracy of each energy level. Does the average number of states per unit energy increase or decrease as E increases?
ANSWER:
Solution 14P
Step 1 of 2
The energy for a non relativistic particle in a three dimensional box is
=
(
Where, = Planck’s constant ,
is the mass of the particle,
is the length of the cubic box ,\
,
,
=
All states with energies below 15 are as follows
For () = (1,1,1) the energy of the particle is
= 3
For () = (1,1,2) (1,2,1) (2,1,1) the energy of the particle is
= 6
For () = (1,2,2) (2,1,2) (2,2,1) the energy of the particle iss
= 9
For () = (1,1,3) (1,3,1) (3,1,1) the energy of the particle is
= 11
For () = (2,2,2) the energy of the particle is
= 12
For () = (1,2,3) (1,3,2) (2,1,3) (2,3,1) (3,1,2) (3,2,1) the energy of the particle is
= 14
is as shown in the fig.