Finite potential well easy question

[frozenguy]

Homework Statement

1.) A particle of kinetic energy 50 eV in free space travels into a region with a potential well of depth 40 eV. What happens to its speed?
a.) it stays the same
b) it increases in the region of the well
c) it decreases in the region of the well
d) not enough information given


2.) A particle of kinetic energy 50 eV in free space travels into a region with a potential well of depth 40 eV. What happens to its wavelength?
a) it stays the same
b) it increases 50%
c) it becomes 2/3 of its value in free space
d) none of the above

The Attempt at a Solution

1.) Is this like a bowling ball coming up to a dip?
I would say b the speed increases.

2.) If the speed increases, than its wavelength decreases, so I say either c or d.
But I feel very uncomfortable with these answers and I'm not confident. I want to be confident..

Thanks in advance!

 

[ideasrule]

1.) Is this like a bowling ball coming up to a dip?
I would say b the speed increases.

Yes, that's right.

2.) If the speed increases, than its wavelength decreases, so I say either c or d.

That's also right, but which one is it? The de Broglie wavelength is h/p, and if you express p in terms of total kinetic energy, you can easily find the ratio between the new wavelength and the old one.

 

[frozenguy]

Yes, that's right.



That's also right, but which one is it? The de Broglie wavelength is h/p, and if you express p in terms of total kinetic energy, you can easily find the ratio between the new wavelength and the old one.

Thanks for the response :)

p=sqrt(2mK)

So lambda =h/sqrt(2mK)
and lambda'= h/sqrt(2mK')

$$\lambda' = \lambda \frac{\sqrt{K}}{\sqrt{K'}}$$

And K=50 with K'=90?
With that I get lambda' = 0.745(lambda)
Considering I did that right, I choose d.