A quantum particle of mass m1 is in a square well with infinitely high walls and

Question

A quantum particle of mass m1 is in a square well with infinitely high walls and length 3 nm. Rank the situations (a) through (e) according to the particle?s energy from highest to lowest, noting any cases of equality. (a) The particle of mass m1 is in the ground state of the well. (b) The same particle is in the n = 2 excited state of the same well. (c) A particle with mass 2m1 is in the ground state of the same well. (d) A particle of mass m1 in the ground state of the same well, and the uncertainty principle has become inoperative; that is, Planck?s constant has been reduced to zero. (e) A particle of mass m1 is in the ground state of a well of length 6 nm. (Use only ''>'' or ''='' symbols. Do not include any parentheses around the letters or symbols.) A particle in a rigid box of length L is in the first excited state for which n = 2 (see figure below). Where is the particle most likely to be found? at the center of the box

Explanation / Answer

Energy = E = n^2 h^2 / 8 m L^2

a) mass m1 and ground state , n = 1

E = h^2 / 8 m1 L^2

b) mass m1 and excited state, n = 2

E = 2^2 h^2 / 8 m L^2 = 4 h^2 / 8 m1 L^2

c) mass 2m1 and ground state, n = 1

E = n^2 h^2 / 8 m L^2 = h^2 / ( 8 * 2m1 L^2 ) = 0.5 h^2 / 8 m1 L^2

d) h = 0

E = n^2 h^2 / 8 m L^2 = 0

e) Length = 2 L

E =  h^2 / 8 m (2L)^2 = 0.25 h^2 / 8 m1 L^2

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b > a > c > e > d

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