Answer:
approximately 21.05 mg.
Explanation:
The mass of a radioactive particle at any given time can be calculated using the following formula:
m(t) = m(0) * (1/2)^(t/T)
where:
m(t) = mass of the particle at time t
m(0) = initial mass of the particle
t = time elapsed since the start of the decay process
T = half-life of the particle
Using this formula, we can solve the given problem as follows:
a. The mass at t=0:
Since we are given the initial mass of the particle, we can simply state that:
m(0) = 50 mg
b. Its mass after 40 minutes:
We can use the formula above to calculate the mass of the particle after 40 minutes:
m(40) = m(0) * (1/2)^(40/30)
m(40) = 50 * (1/2)^(4/3)
m(40) = 50 * 0.421
m(40) = 21.05 mg (rounded to two decimal places)
Therefore, the mass of the particle after 40 minutes is approximately 21.05 mg.