Question

A beam of neutrons moving with speed of 1450 m/s is diffracted from a crystal of table salt, which has an interplanar spacing of d=0.282 nm.

a) Find the de Broglie wavelength of the neutrons.

b) Find the angle of the first interference maximum.

c) What happens if the speed of the neutrons changes?

Answer 1

Speed of beam v = 1450 m/s

interplanar spacing d=0.282 nm.= 2.82*10^-10 m

(A) De broglie equation

= h/p = h/mv

where m is the mass of neutron = 1.67*10^-27

= (6.62*10^-34)/{(1.67 x 10^-27)(1450)}

= 2.733*10^-10 m or 0.2733 nm

(B) we know that

2d*sin= m

m =1 (first interference maxima )

{2*(0.282*sin} = 1*0.2733

sin = 0.48

= 28.69 degree

(C)  The wavelength is equal to Planck’s constant (h) divided by the momentum (P), and the velocity increases with the momentum (although not linearly when the speed gets relativistic). Therefore the wavelength decreases as the speed increase.

1/V