Answer:
3
Explanation:
The half-life of a radioactive isotope is the time it takes for the mass of the sample to halve.
This can be rewritten as follows:
where
m(t) is the mass of the sample at time t
m0 is the original mass of the sample
n is the number of half-lives that passed
We see that if we take n=3, the amount of original sample left is
So 3 (3 half-lives) is the correct answer.
Answer:
The time constant is
Explanation:
From the question we are told that
The spring constant is
The mass of the ball is
The amplitude of the oscillation t the beginning is
The amplitude after time t is
The number of oscillation is
Generally the time taken to attain the second amplitude is mathematically represented as
Here T is the period of oscillation
=>
=>
Generally the amplitude at time t is mathematically represented as
Here a is the damping constant so
at ,
So
=>
taking natural log of both sides
=>
=>
Generally the time constant is mathematically represented as
=>
=>