A radioactive element x has half life of 30 days and will decay to become another new element Y..
a) calculate decay constant
b) how long it will take for 90% of the no.Of atom in radioisotope x to decay?
To calculate the decay constant, you can use the formula:
λ = ln(2) / T½
where λ is the decay constant and T½ is the half-life of the radioactive element.
a) Calculating the decay constant:
Given that the half-life (T½) of the radioactive element X is 30 days, we can substitute this value into the formula:
λ = ln(2) / 30
Plugging this into a calculator, we get:
λ ≈ 0.0231 per day
Therefore, the decay constant is approximately 0.0231 per day.
b) To determine how long it will take for 90% of the atoms in radioisotope X to decay, you can use the exponential decay equation:
N(t) = N₀ * e^(-λt)
where N(t) is the number of atoms remaining at time t, N₀ is the initial number of atoms, λ is the decay constant, and e is the base of the natural logarithm.
In this case, we want to find the time (t) at which 90% of the atoms decay, so N(t) / N₀ = 0.1.
0.1 = e^(-λt)
We can rearrange this equation to solve for t:
t = ln(0.1) / -λ
Plugging in the value of the decay constant from part a), we get:
t ≈ ln(0.1) / (-0.0231)
Using a calculator, the result is approximately:
t ≈ 104.3 days
So, it will take approximately 104.3 days for 90% of the atoms in radioisotope X to decay.