Question

In 1924, Prince Louis de Broglie suggested that all moving particles demonstrate wave-like

behaviour.
a) State the de Broglie equation and define all the symbols.
b) Neutrons may be used to study the atomic structure of matter. Diffraction effects are
noticeable when the de Broglie wavelength of the neutrons is comparable to the spacing
between the atoms. This spacing is typically 2.6 x 10-10 m.
i. Suggest why using neutrons may be preferable to using electrons when investigating
matter.
ii.
Calculate the speed (v) of a neutron having a de Broglie wavelength of
2.6 x 10-¹0 m. The mass of a neutron is 1.7 x 10-27 kg.

Answer 1

a) The de Broglie equation is λ = h/mv, where λ is the wavelength of a particle, h is Planck's constant (6.626 x 10^-34 J s), m is the mass of the particle, and v is its velocity.

b) Neutrons may be preferable to electrons when investigating matter because neutrons have a higher penetrating power than electrons and can pass through thicker samples. Neutrons also interact differently with matter than electrons, allowing them to provide unique information about the atomic structure of materials.

To calculate the speed of a neutron with a de Broglie wavelength of 2.6 x 10^-10 m, we can rearrange the de Broglie equation to solve for v:

v = h/(mλ)

Plugging in the values, we get:

v = (6.626 x 10^-34 J s) / (1.7 x 10^-27 kg x 2.6 x 10^-10 m)

v = 1.56 x 10^3 m/s

Therefore, the speed of the neutron is approximately 1.56 x 10^3 m/s.