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Strontium-90 has a half-life of 29 years. In how many years will a 1 kg sample of strontium-90 decay and reduce to 0.25 kg of strontium-90?

Answer


58 years


116 years


87 years


29 years

Verified Answer :

syed514

In 58 (2.29 yrs - 1/2.1/2 .1 kg ) years will a 1 kg sample of strontium-90 decay and reduce to 0.25 kg of strontium-90.
229 years - 1/21/2 *1 kg.

Answer: 58 years

Explanation:
-

Radioactive decay follows first order kinetics.

Half-life of strontium-9 = 29 years

\(\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{29}=0.024year^{-1}\)

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

N = amount left after time t  = 0.25 kg

\(N_0\) = initial amount  = 1 kg

\(\lambda\) = rate constant
= 0.024

t= time  = ?

\(0.25kg=1kg\times e^{- 0.024 years^{-1}\times t years}\)

\(t=58years\)

Thus it takes 58 years to a 1 kg sample of strontium-90 decay and reduce to 0.25 kg of strontium-90.

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