Question

Outside the nucleus, the neutron itself is radioactive and decays into a proton, an electron, and an antineutrino. The half-life of a neutron (mass = 1.675 × 10-27 kg) outside the nucleus is 10.4 min. On average, over what distance x would a beam of 3.39-eV neutrons travel before the number of neutrons decreased to 75.0% of its initial value? Ignore relativistic effects.

Answer 1

lambda = 0.693 / t_1/2 = 0.693 / (10.4 * 60) = 1.11 * 10^-3

0.75 N₀ = N₀ * e^-lambda*t

0.75 = e^-lambda*t

0.287 = lambda * t

t = 0.287 / 1.11 * 10^-3 = 258.5 s

E = 3.39 * 1.6 * 10^-19 = 5.42 * 10^-19 J

1/2 m v² = 5.42 * 10^-19

v = sqrt [2 * 5.42 * 10^-19 / 1.675 * 10^-27] = 25439 m/s

distance x = v t = 25439 * 258.5

= 6.57 * 10⁶ m