Particle in a Box: Calculating P from 0 to 0.2 nm

[ahhppull]

Homework Statement

What is the probability, P, of locating a particle between x = 0 (the left-hand end of
a box) and x = 0.2 nm in its lowest energy state in a box of length 1.0 nm?

Homework Equations

Probability = ∫ψ²dx
ψ = (2/L)^1/2sin(n∏x)

The Attempt at a Solution

ψ² = (2/L)sin²(n∏x)
∫(2/L)sin²(n∏x)dx = 2/L [x/2 - (L/n∏x)sin(2n∏x/L)] from x = 0 to x = 0.2

I plugged in the numbers n=1 and L = 1 and got about 0.2.
The answer is 0.05.

 

[TSny]

ψ² = (2/L)sin²(n∏x)
∫(2/L)sin²(n∏x)dx = 2/L [x/2 - (L/n∏x)sin(2n∏x/L)] from x = 0 to x = 0.2

Check the factor highlighted above. Note that this factor should have the dimensions of length.

 

[lep11]

Isn't this advanced physics?

 

[TSny]

Isn't this advanced physics?

Not necessarily. The particle in a box is often covered in the introductory calculus-based physics course (usually in the 3rd semester of the course in the U.S.).

 

[ahhppull]

Check the factor highlighted above. Note that this factor should have the dimensions of length.

I still don't understand.

I may have wrote something wrong.
The part that you highlighted should be: (L/n∏)

 

[ahhppull]

I got the answer now, but by changing my calculator to radians when calculating sin(2n∏x/L). Am I suppose to use radian instead of degrees?

 

[tia89]

Yes you are... you are working with numbers here, not with angles... in this case the sine is just a function, and want an adimensional argument. While radians are a conventional unit for angles but are not a real units (you call radians to understand that you are speaking of angles but it is still a pure number), degrees are indeed an unit, so you can't use them here

 

[Rooted]

Yes, well done, you're right, radians always for this sort of thing. Took me ages to get used to that.

 

[ahhppull]

Yes you are... you are working with numbers here, not with angles... in this case the sine is just a function, and want an adimensional argument. While radians are a conventional unit for angles but are not a real units (you call radians to understand that you are speaking of angles but it is still a pure number), degrees are indeed an unit, so you can't use them here

Ok...Thanks!