Simple positron diffraction problem

[asdf12312]

Homework Statement

A beam of positrons (positron ≡ antielectron) travels at 0.001% the speed of light and impinges on a slit that is 1 μm wide. Use modern units to find the angle θ between the center line and 3rd minimum of the resulting diffraction pattern. How far away (in cm) would you locate a detector so that the 3rd minimum is spaced 20 cm from the center line?

Homework Equations

wavelength = hc/pc where hc=1240nm*ev
and i believe p=mv where mass is same as electron =9.1e-31 and so pc=mc²=0.511e6

there is example in my notes where pc=mv*c=mc²(v/c) was used to find wavelength if v was given in % of c. but this is where I get confused because in the notes 0.1%*c becomes 0.001 somehow (10^-2?)

for minima: (n-0.5)*wavelength=d*sin(θ) where asked to find θ, d=1e-6m and n=3 for this problem.

The Attempt at a Solution

so.. after various incorrect attempts it give me what the answer should be but problem is I don't know how to get it :(

θ = 46.7200 Degrees
Tries 3/3
L= 18.8339 cm
Tries 3/3

I think i should do something like find wavelength using 1240/(0.511e6*0.001) and if I do I get 2.43 nm. but i think I am doing it wrong because I get wrong θ :(

 

[mfb]

but this is where I get confused because in the notes 0.1%*c becomes 0.001 somehow (10^-2?)

Sure.
100% = 1
10% = .1
1% = .01
and so on.

 

[strugglebus3]

You used the wrong equation to find the angle. This is a question about diffraction, not interference. Your equation for the minima should be nλ=asinθ, where a is the slit width (in this case a=1e-6 m) and n=3.
Your wavelength equation is correct. Wavelength should equal 242.7 nm.
Use Y=Ltanθ to find L.
20 cm is your vertical displacement from center line.