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Chapter 28: Q6PE (page 1029)

A neutron lives 900 s when at rest relative to an observer. How fast is the neutron moving relative to an observer who measures its life span to be 2065s?

Short Answer

Expert verified

The neutron is moving relative to an observer at the velocity of 900c.

Step by step solution

01

To find the velocity

The life of the neutron when relative to an observer i.e., proper time is

∆t0= 900s

The life of the neutron when measured in the laboratory

∆t= 2065 s

we have

\[\Delta t = \frac{{\Delta {t_0}}}{{\sqrt {1 - {{\left( {\frac{v}{c}} \right)}^2}} }}\] - (1)

Where v is its velocity relative to an observer and c= 3.00 × 108 ms-1 is the speed of the light

02

To solve the equation

From the above equation (1), we get

\begin{aligned}v = c\sqrt {1 - {{\left( {\frac{{\Delta {t_0}}}{{\Delta t}}} \right)}^2}} \\= c\sqrt {1 - {{\left( {\frac{{900s}}{{2065s}}} \right)}^2}} \\= 0.900c\end{aligned}

Hence the neutron moving relative to an observer in the velocity of v= 0.900 c .

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