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

Chemistry

1 answer:

olya-2409 [2.1K]3 years ago

3 0

It will take 42.9 days

<h3>Further explanation</h3>

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

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

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