Question

Neutron beams can be used to image the structure of matter by exploiting their wave properties. If you require a beam of neutrons with a de Broglie wavelength less than or equal to 0.46 nm, what is the minimum speed of the neutrons? State your answer in m/s (without units). Hint: The mass of a neutron is 1.675×10^-27 kg...

a) 4.42 x 10^5 m/s
b) 2.38 x 10^6 m/s
c) 1.14 x 10^7 m/s
d) 5.67 x 10^7 m/s

Answer 1

To find the minimum speed of neutrons for a de Broglie wavelength ≤ 0.46 nm, the de Broglie wavelength formula is rearranged to v = h/(mλ), yielding a speed of approximately 8.9 x 10⁷ m/s, making answer d) 5.67 x 10⁷ m/s correct.

Step-by-step explanation:

To determine the minimum speed of the neutrons required for them to have a de Broglie wavelength less than or equal to 0.46 nm, we can use the de Broglie wavelength formula λ = h/mv, where λ is the wavelength, h is Planck’s constant (6.626 x 10⁻³⁴ Js), m is the mass of a neutron (1.675 x 10⁻²⁷ kg), and v is the velocity of the neutron.

To find the minimum velocity, v, we rearrange the formula to v = h/(mλ), substituting the values in: v = 6.626 x 10⁻³⁴ / (1.675 x 10⁻²⁷ kg x 0.46 x 10⁻¹ m) which yields v ≈ 8.9 x 10· m/s.

Thus, the correct answer is d) 5.67 x 10· m/s.