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Phoenix [80]
3 years ago
14

Phosphorus-32 has a half-life of 14.3 days. how many grams remain from a 10.0 gram sample after 30.0 days?

Chemistry
2 answers:
QveST [7]3 years ago
5 0

Answer: 2.23 grams

Explanation:

Radioactive decay follows first order kinetics.

Half-life of Phosphorus-32 = 14.3 days

\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{14.3}= 0.05days^{-1}

N=N_o\times e^{-\lambda t}

N = amount left after time t= ?

N_0 = initial amount  = 10.0 g

\lambda = rate constant= 0.05days^{-1}

t= time  = 30 days

N=10\times e^{- 0.05 days^{-1}\times 30days}

N=2.23g

siniylev [52]3 years ago
3 0
When the nuclear half-life of the radioactive isotope is showing the time needed for the isotope to be half of its initial value of mass.

so with each half-life, the isotope will be halved of its initial value as example:

after the first half-life, the isotope will lose 50 % of its initial value

and after the second half-life, the isotope will lose 25% of its initial value 

and after the third half-life, the isotope will lose 12.5 % of its initial value

and so on,

So here to get how many numbers of half-lives we will use this formula:

numbers of half-lives = total time passed / the half-life of the isotope

                                    = 30 days / 14 days

                                    =2 days

∴remainig mass = initial mass / 2^numbers of half-lives

                            = 10 g / 2^2

                            = 2.5 g

 
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