Pions have a half-life of 1.8 x 10^-8 s. a pion beam leaves an accelerator at a speed of 0.8c. what is the expected distance over which half the pions should decay?

the expected distance is 4.32 m

Explanation:

given data

half life time = 1.8 × s

speed = 0.8 c = 0.8 × 3 ×

to find out

expected distance over

solution

we know c is speed of light in air is 3 × m/s

we calculate expected distance by given formula that is

expected distance = half life time × speed   .........1

put here all these value

expected distance = half life time × speed

expected distance = 1.8 × ×  0.8 × 3 ×

expected distance = 4.32

so the expected distance is 4.32 m

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2