Neutrons travelling at 0.400 m/s are directed through a pair of slits having 1.00 m separation. an array of detectors is placed 10.0 m from the slits. a) What is the de Broglie wavelength of the neutrons?
b) How far off axis if the first zero-intensity point on the detector array?
c) When a neutron reaches a detector, can we say which slit the neutrons passed through? Explain.

9.91*10^-7 m

4.955*10^-6 m

Explanation:

Given that

v = 0.4 m/s

d = 1 m

L = 10 m

h = 6.62*10^-34 Js

m(neutron) = 1.67*10^-27 kg

To find the debroglie wavelength of the neutron, we use the formula

λ = h/mv

Now, we plug in the values we have listed.

λ = 6.62*10^-34 / (1.67*10^-27 * 0.4)

λ = 6.62*10^-34 / 6.68*10^-28

λ = 9.91*10^-7 m

b)

y1 = L (m + ½) λ/d, where m = 0

y1 = L (0 + ½) λ/d

y1 = L (½) λ/d

y1 = L/2 * λ/d or

y1 = Lλ/2d

now, we substitute the values for each of them, we have

y1 = (10 * 9.91*10^-7) / (2 * 1)

y1 = 9.91*10^-6 / 2

y1 = 4.955*10^-6 m

c) no, we can not say the neuron passed through one slit