Question

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

radioactive sample to decay to one-eighth its original size?

Answer 1

It will take 42.9 days

Further explanation

General formulas used in decay:

`\large{\boxed{\bold{N_t=N_0((1)/(2))^{T/t(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((1)/(2))^(T/t1/2)\\\\(Nt)/(No)=(1)/(2)^(T/t1/2)\\\\(1)/(8)=(1)/(2)^(T/t1/2)\\\\((1)/(2))^3=(1)/(2)^(T/t1/2)\\\\3=T/14.3\rightarrow T=42.9~days`