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kumpel [21]
3 years ago
12

If the half-life of technitium-104 is 18.0 min, how much of a 14.2-g sample will remain after 72 minutes?

Chemistry
2 answers:
sergij07 [2.7K]3 years ago
7 0

Answer : The correct option is, 0.888 g

Solution : Given,

As we know that the radioactive decays follow first order kinetics.

First we have to calculate the rate constant of a radioisotope.

Formula used : t_{1/2}=\frac{0.693}{k}

18min=\frac{0.693}{k}

k=0.0385min^{-1}

Now we have to calculate the amount remains after 72 minutes.

The expression for rate law for first order kinetics is given by :

k=\frac{2.303}{t}\log\frac{a}{a-x}

where,

k = rate constant  = 0.0385min^{-1}

t = time taken for decay process  = 72 min

a = initial amount of the reactant  = 14.2 g

a - x = amount left after decay process  = ?

Putting values in above equation, we get the value of amount left.

0.0385min^{-1}=\frac{2.303}{72min}\log\frac{14.2g}{a-x}

a-x=0.888g

Therefore, the amount remain after 72 min will be, 0.888 g

Debora [2.8K]3 years ago
3 0
The decay of a radioactive isotope can be predicted using the formula: A = Ao[2^(-t/T_0.5)] where A is the amount after time t, Ao is the original amount and T_0.5 is the half-life. Using the equation and the given values, 0.888 g of the sample will remain after 72 minutes. 
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