3 half-lives have occured
Given
Half-life Radon-222 = 3.8 days
12.5% of Rn-222 remains
Required
Half-lives occurred
Solution
General formulas used in decay:
[tex]\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{t/t\frac{1}{2} }}}[/tex]
T = duration of decay
t 1/2 = half-life
N₀ = the number of initial radioactive atoms
Nt = the number of radioactive atoms left after decaying during T time
12.5% of Rn-222 remains ⇒ Nt/No = 0.125
Input the value :
[tex]\tt 0.125=\dfrac{1}{2}^{t/3.8}\\\\\dfrac{1}{2}^3=\dfrac{1}{2}^{t/3.8}\\\\3=t/3.8\\\\t=11.4\rightarrow 3~half-lives[/tex]
