- #1

Zeynaz

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- Homework Statement
- A ball of mass 3 g is trapped in a box with infinitely high walls. The width of the box is 8 cm.

a) Calculate the speed of the ball when it is in the ground state of the box

b)Estimate the quantum number n if the ball is moving with a constant speed of 2 m/s in the box

- Relevant Equations
- Ek= 1/2 (m)(v)^2

E=hf

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

I am having difficulties understanding this concept. Particle in a box (as far as i understood) shows that the electrons or particles need a certain about of potential energy to escape the one-dimentional potential well. I think its pretty similar to the concept of the electons and ionising energies. (correct me if i am wrong).

so in question a) i tried to use the formula by just using the values i knew, L=0.08 m and m=3e-3 kg. I also took n=1.

As a result E=4.32e-30 J. When i equate this energy with KE. I get a small velocity of 3m/s. (The correct answer is 1.0e-30 m/s)

I am not sure how to find the right answer.

Also, because the ball is in a box with infinitely high walls, it should have an infinite potential energy thus inifinite KE. So how is it possible to find a value for this.

can someone explain/help?

thanks!

so in question a) i tried to use the formula by just using the values i knew, L=0.08 m and m=3e-3 kg. I also took n=1.

As a result E=4.32e-30 J. When i equate this energy with KE. I get a small velocity of 3m/s. (The correct answer is 1.0e-30 m/s)

I am not sure how to find the right answer.

Also, because the ball is in a box with infinitely high walls, it should have an infinite potential energy thus inifinite KE. So how is it possible to find a value for this.

can someone explain/help?

thanks!