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1. A particle is confined to be within a rectangular box of dimensions 1cm x1cm

ID: 3896649 • Letter: 1

Question

1.     A particle is confined to be within a rectangular box of dimensions 1cm x1cm x 2cm. The magnitude of its momentum is constrained to be less than 3x10-24 kg m/s. What is the probability that it is in any one particular quantum state. What is the probability that the magnitude of its momentum is less than 2 x 10-24 kg m/s? What is the probability that the magnitude of its momentum is greater than 10-24 kg m/s and less than 3x10-24 kg m/s AND that it is in the right half of the box? ans: a)1.3x10^-24 b).30 c).48

Explanation / Answer

1) probablity = 3x10-24/sqrt(1^2+1^2+2^2)

= 1.3x10^-24

2) P= v1^3/v^3

= 2^3/3^3= 8/27

= 0.3

c)

P = (1-1^3/3^3)/2

= 1-1/27)/2

= 0.48