Question

Phosphorus-32 has a half life of 14.3 days. How many days will it take for a

Answer 1

It will take 42.9 days

Further explanation

General formulas used in decay:  

$\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{T/t\frac{1}{2} }}}$

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  

t1/2=14.3 days

Nt/No=1/8

$\tt Nt=No(\dfrac{1}{2})^{T/t1/2}\\\\\dfrac{Nt}{No}=\dfrac{1}{2}^{T/t1/2}\\\\\dfrac{1}{8}=\dfrac{1}{2}^{T/t1/2}\\\\(\dfrac{1}{2})^3=\dfrac{1}{2}^{T/t1/2}\\\\3=T/14.3\rightarrow T=42.9~days$