PX156 - B3 - de broglie hypothesis

de broglie hypothesis: matter can exhibit wave-like properties
de broglie wavelength:

λ = \frac{h}{p}; p = \frac{h}{λ} = ℏ k

for the same speed, the lighter particle will have a smaller momentum and therefore a longer de broglie wavelength

L = r p = \frac{n h}{2 π} = n ℏ ⟹ r \frac{h}{λ} = \frac{n h}{2 π} ⟹ n λ = 2 π r

when x-rays are incident on a lattice plane:

$d =$ inter-planar spacing
$2 θ =$ scattering angle
$θ =$ bragg angle
bragg's law:

n λ = 2 d \sin θ

for $λ \approx d s p a c i n g$

neutron scattering

fission:

n +^{235} U \to^{91} K r +^{142} B a + 2 n

spallation:

p + W \to 20 / 30 n

considering a neutron with speed, $v = 10^{6} m s^{- 1}$
$λ = \frac{h}{p} \approx 0.004 Å$
$λ \approx d s p a c i n g$
consider a grain of sand:
$m = 10 m g$ , $v \sim 100 m s^{- 1}$
$λ = \frac{h}{p} \approx 6.63 \times 10^{- 34} m$
- the wave description and particle description are complementary. both are required to model the nature properly