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A cubic crystal of interatomic spacing of 0.24 nm is used to select

gamma–rays of energy 100 keV from a radioactive source containing a continuum of energies. If the incident beam is normal to the crystal, at

what angle with respect to the incident beam do the 100 keV gamma–rays appear?

2. Equations and Variables

Bragg's Law: n(lambda) = 2dsinx

n is the order of intensity

lamba is the wavelength

d is the Bragg plane separation

x is the angle

E is energy, E=100keV=1.60x10^-14J

3. Attempt

Since the incident beam is normal to the crystal, d=0.24nm.

E=hf

E=h(c/lambda)

lambda=(hc)/E

=(6.626x10^-34)(3.00x10^8)/1.60x10^-14

=1.24x10^-11m

sinx=n(lambda)/2d

=[1(1.24x10^-11)]/[2(0.24x10^-9)]

= 0.0258

x = 1.48 degrees.

Just a bit unsure of myself. I guess it's the theory that is troubling me. I thought that the angle of incidence equals the angle of deflection. Thanks fellas.