The new half-life of the radioactive particle, as observed from a reference frame in which it is moving at 3/5 the speed of light, is 4/5 seconds.
In special relativity, the concept of time dilation states that time appears to pass more slowly for objects moving at high speeds relative to an observer. This means that the perceived half-life of a radioactive particle can be affected by its velocity.
To calculate the new half-life of a radioactive particle moving at 3/5 the speed of light, we need to take into account the time dilation effect. The formula for time dilation in special relativity is:
[tex]t' = t / γ[/tex]
Where:
t' is the observed time interval (half-life) in the moving frame of reference.
t is the proper time interval (half-life) in the rest frame of reference.
γ (gamma) is the Lorentz factor, given by [tex]γ = 1 / sqrt(1 - v^2/c^2)[/tex], where v is the velocity of the particle and c is the speed of light.
In this case, we know that the proper half-life (t) of the radioactive particle is 1 second. The velocity (v) is 3/5 times the speed of light (c). Therefore:
v = (3/5) * c
We can substitute these values into the formula for γ and calculate the Lorentz factor:
[tex]γ = 1 / sqrt(1 - v^2/c^2)γ = 1 / sqrt(1 - ((3/5)^2 * c^2) / c^2)γ = 1 / sqrt(1 - 9/25)γ = 1 / sqrt(16/25)γ = 1 / (4/5)γ = 5/4[/tex]
Now we can calculate the observed half-life (t') using the time dilation formula:
[tex]t' = t / γt' = 1 s / (5/4)t' = 4/5 s[/tex]
Therefore, the new half-life of the radioactive particle is 4/5 seconds.
To learn more about radioactive, refer below:
https://brainly.com/question/1770619
#SPJ11