High School

We appreciate your visit to A tutoring company states that isolated neutrons outside the nucleus are unstable After a typical lifetime of about 15 minutes they decay into a proton. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A tutoring company states that isolated neutrons outside the nucleus are unstable. After a typical lifetime of about 15 minutes, they decay into a proton and another particle called a neutrino.

Consider a neutron that has a lifetime of 900 seconds when at rest relative to an observer. How fast is the neutron moving relative to an observer who measures its lifespan to be 2065 seconds?

Answer :

According to time dilation, the elapsed time between two events is different for observers in relative motion to each other. The formula for time dilation is given by:

Δt' = Δt / sqrt(1 - v^2/c^2)

where Δt is the time interval measured by the observer in the rest frame, Δt' is the time interval measured by the observer in the moving frame, v is the relative velocity between the two frames, and c is the speed of light.

In this problem, the neutron is at rest relative to the first observer and its lifetime is measured to be 900 s. The neutron is moving relative to the second observer, and its lifetime is measured to be 2065 s. We want to find the velocity v of the neutron relative to the second observer.

We can use the time dilation formula twice, once for each observer:

Δt' = Δt / sqrt(1 - v^2/c^2)

For the first observer (rest frame of the neutron), Δt = 900 s and Δt' = 2065 s (measured by the second observer):

2065 = 900 / sqrt(1 - v^2/c^2)

Simplifying and rearranging:

(1 - v^2/c^2) = (900/2065)^2

1 - v^2/c^2 = 0.155

v^2/c^2 = 0.845

v/c = sqrt(0.845)

v = 0.919c

Therefore, the neutron is moving at a speed of 0.919 times the speed of light relative to the second observer.

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