The lifetime of the neutron will be t=40 minutes when the neutron is moving at a speed of 936 c.
when neutrons are free and floating alone outside of an atom, they start to decay into protons and other particles.The formula for the life of the neutron will be given by:
[tex]t=\dfrac{\Delta t_o}{\sqrt{1-\dfrac{v^2}{c^2}}}[/tex]
Here
t= Lifetime
to=Average life
v= velocity
c=speed of light
Since the average life of the neutron is about 14 minutes or 840 seconds.
Velocity =0.936c
By putting the values in the question
[tex]t=\dfrac{840}{\sqrt{1-\dfrac{(0.936c)^2}{c^2}}}[/tex]
[tex]t=\dfrac{840}{\sqrt{0.123}}[/tex]
[tex]t=\dfrac{840}{0.35}=2400\ \ sec\\\\[/tex]
Hence the lifetime of the neutron will be t=40 minutes when the neutron is moving at a speed of 936 c.
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