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** ^{235}**U isotopes. Calculate the
wavelength (in nm) associated with a beam of neutrons moving at
6.95** × **10**^{2} **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*10^{2} m/s) = (6.62*10^{-34}
kg.m^{2}/s)/(1.675*10^{-27}
kg).(6.95*10^{2} 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.m^{2}/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).

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