Question

A ?+ is a subatomic particle called a Pion that is positively charged. It has a mean lifetime of about 26 ns (26x10-9 s) as measured in the pion's frame of reference. Suppose a pion is created in the atmosphere and is moving at 0.856c relative to a stationary observer on Earth. How far in meters does the pion travel during its lifetime according to the Earth-bound observer? Assume 3 significant figures.

The formula d=speed x time DOES NOT WORK FOR THIS QUESTION. Please explain the correct way to do this problem using the right formula. thank you

Answer 1

since the pion is travelling at a speed close to the speed of light, simple basic formulas are not used to calculate the variables. We need to use Einsteins special theory of relativity which for a particle travelling at speed close to speed of light has a different expression.

since ,the observer is stationary at earth, the lifetime measured by the observer would be completely different from what the original lifetime is,
we have

where,

t₀ is the given lifetime = 26 ns = 26 x 10^-9 s

t is the lifetime measured by observer on earth,

v = speed of pion 0.856 c

c=speed of light = 3 x 10⁸ m/s

thus, we get

now, we need to calculate the distance the pion travels which is simply given by

d = v*t = 0.856c*(9.74 x 10^-8) m = 0.856*(3 x 10⁸ m/s)*((9.74 x 10^-8) = 25.01 m