Question

A particle in a box of length L. has energy E1- 2.0 eV. The same particle in a box of length Lb has energy E,-50.0 eV. a. What is the ratio La/ Lb? Show your working. The figure below shows a standing de Broglie wave b. Does this standing wave represent a particle that travels back and forth between the boundaries with a constant speed or a changing speed? Support your answer with an appropriate explanation. c. If the speed is changing, at which end (left or right) is the particle moving faster and at which end it is moving slower? Support your answer with an appropriate explanation. A golf ball has a mass of 0.045 kg and speed of 35 ms-1. This speed can be measured to a precision of 1.5%. Assuming the golf ball is moving in the x-direction. What limit does Heisenberg's Uncertainty Principle place on your ability to measure the position of the golf ball? Show your working. d.

Answer 1

(a) We know

E=n^2h^2/8mL^2

So it is inversly proportional to L^2

so

La/Lb=sqrt(E2/E1)=5:1

(b) As we can frequency or time period of wave is not constant so it is not same

(c)Assuming wavelength is same for wave

Speed is fast to left side as here frequency is more and velocity=frequency*wavelength