Part A Find the lowest energy level for a particle in a box if the particle is a

Question

Part A

Find the lowest energy level for a particle in a box if the particle is a billiard ball (m=0.200 kg) and the box has a width of 1.5 m, the size of a billiard table. (Assume that the billiard ball slides without friction rather than rolls. That is, ignore the rotational kinetic energy.)

Express your answer using two significant figures.

Part B

Since the energy in part (A) is all kinetic, to what speed does this correspond?

Express your answer using two significant figures.

Part C

How much time would it take at this speed for the ball to move from one side of the table to the other?

Express your answer using two significant figures.

Explanation / Answer

mass = m = 0.2 kg

length = L = 1.5 m

h = 6.63 x 10^-34 J s

part A)

Lowest energy for the particle = h^2 / ( 8 m L^2) = (6.63 x 10^-34)^2 / (8*0.2*1.5^2) = 1.22 x 10^-67 J

part B)

0.5 mv^2 = 1.22 x 10^-67

v = sqrt((1.22*10^-67)/(0.5*0.2)) = 1.105 x 10^-33 m/s

part C

time taken = distance / speed = 1.5 / (1.105 x 10^-33) = 1.357 x 10^33 s

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Answers

A) lowest energy level = 1.2 x 10 -67 J

B) Speed = 1.1 x 10 -33 m/s

C) Time taken = 1.4 x 10 33 s

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