Question

Thermal neutrons are neutrons that move at speeds comparable to those of air molecules at room temperature. These neutrons are most effective in initiating a nuclear chain reaction among ²³⁵U isotopes. Calculate the wavelength (in nm) associated with a beam of neutrons moving at 6.95 × 10² m/s (mass of a neutron =1.675 ×10⁻²⁷ kg). Enter your answer in scientific notation.

What is the de Broglie wavelength, in cm, of a 11.1−g hummingbird flying at 105 mph? (1 mile = 1.61 km.)

Answer 1

Use the de-Broglie equation as

λ = h/mv where λ= wavelength of the neutron, m is the mass of the neutron and v is the velocity of the neutron; h is Planck’s constant = 6.62*10^-34 J.s.

Plug in values to obtain

λ = (6.62*10^-34 J.s)/(1.675*10^-27 kg).(6.95*10² m/s) = (6.62*10^-34 kg.m²/s)/(1.675*10^-27 kg).(6.95*10² m/s) = 5.686*10^-10 m ≈ 5.7*10^-10 m = (5.7*10^-10 m)*(1 nm/1.0*10^-9 m) [1 nm = 1.0*10^-9 m] = 0.57 nm (ans).

The speed of the bird is 105 mph = (105 mph)*(1.61 km/1 mile) = 169.05 kmph = (169.05 km)/(1 hr) = (169.05*1000 m)/(3600 s) = 46.9583 m/s.

Mass of the bird = 11.1 g = (11.1 g)*(1 kg/1000 g) = 0.0111 kg.

Use the de-Broglie equation to obtain

λ = h/mv = (6.62*10^-34 kg.m²/s)/(0.0111 kg).(46.9583 m/s) = 1.27*10^-33 m = (1.27*10^-33 m)*(1 cm/10^-2 m) = 1.27*10^-31 cm (ans).