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?
a.) Having decay constant as t=0.693/decay constant. Therefore decay constant=0.693/t (i.e time).
Decay constant=0.693/30
=0.02
a.) Having decay constant as t=0.693/decay constant. Therefore decay constant=0.693/t (i.e time).
Decay constant=0.693/30
=0.02
To answer these questions, we need to use the formula for radioactive decay:
N = N0 * e^(-λ * t)
where:
N = final number of atoms
N0 = initial number of atoms
λ = decay constant
t = time
a) To calculate the decay constant (λ), we can use the formula:
λ = ln(2) / t1/2
Given that the half-life (t1/2) of element x is 30 days, we can substitute it into the formula:
λ = ln(2) / 30
Calculating λ:
λ = 0.0231 (approximately)
Therefore, the decay constant (λ) for element x is 0.0231.
b) To find the time it takes for 90% of the atoms to decay, we can start by rearranging the radioactive decay formula:
N/N0 = e^(-λ * t)
Given that we want 90% of the atoms to decay, N/N0 will be 0.1. Substituting the values:
0.1 = e^(-0.0231 * t)
To solve for t (time), we need to take the natural logarithm (ln) of both sides:
ln(0.1) = -0.0231 * t
Now we can solve for t:
t = ln(0.1) / (-0.0231)
Calculating t:
t ≈ 100.93 days
Therefore, it will take approximately 100.93 days for 90% of the atoms in radioisotope x to decay.