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Akimi4 [234]
3 years ago
13

If the half-life of 37Rb is 4.7x101 years, how long would it take for 0.5 grams of a 2 gram sample to radioactively decay?

Chemistry
1 answer:
k0ka [10]3 years ago
4 0

<u>Answer:</u> The time required will be 19.18 years

<u>Explanation:</u>

All the radioactive reactions follows first order kinetics.

The equation used to calculate half life for first order kinetics:

k=\frac{0.693}{t_{1/2}}

We are given:

t_{1/2}=4.7\times 10^1yrs

Putting values in above equation, we get:

k=\frac{0.693}{4.7\times 10^1yr}=0.015yr^{-1}

Rate law expression for first order kinetics is given by the equation:

k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}

where,  

k = rate constant  = 0.015yr^{-1}

t = time taken for decay process = ?

[A_o] = initial amount of the reactant = 2 g

[A] = amount left after decay process =  (2 - 0.5) = 1.5 g

Putting values in above equation, we get:

0.015yr^{-1}=\frac{2.303}{t}\log\frac{2}{1.5}\\\\t=19.18yrs

Hence, the time required will be 19.18 years

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