Consider a three dimensional rectangular infinite potential well with sides of l
ID: 2025473 • Letter: C
Question
Consider a three dimensional rectangular infinite potential well with sides of length L, 2L and 3L.
a).What is the energy of the first excited state relative to the energy of the ground state?
b).What is the energy of the second excited state relative to the energy of the ground state?
c).What is the energy of the third excited state relative to the energy of the ground state?
d).What is the energy of the fourth excited state relative to the energy of the ground state?
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Explanation / Answer
the energy of a particle in a 1-dimensional box of length L is k*n^2/L^2 where k is a constant (h-bar)^2*(pi)^2/(2*mass) and n = 1,2,3,.... the energy of a particle in the 3-d box you described is: k*[ n^2/L^2 + m^2/(2L)^2 + p^2/(3L)^2] n = 1,2,3,.. m = 1,2,3,... p = 1,2,3,... the ground state is at n = m = p =1 with energy k(1/L^2 + 1/[4L^2] + 1/[9L^2]) the first excited energy state is at n = m = 1, p = 2 with an energy difference of k/(3L^2) from the ground state the second excited state is with [n,m,p] = [1,2,1] with an energy difference of 3k/(4L^2) from the ground state the third excited state is with [n,m,p] = [1,1,3] with an energy difference of 8k/(9L^2) from the ground state the fourth excited state is with [n,m,p] = [1,2,2] with an energy difference of k/(3L^2) + 3k/(4L^2) from the ground state