Question

A certain radioactive element has a half-life of one hour. If you start with 20.0 grams of the element at noon, how much of the radioactive element will be left at 3 p.m.?
a. 10.0 grams b. 5.0 grams c. 2.5 grams d. 1.25 grams

Answer 1

Answer: The correct answer is Option c.

Explanation:

All the radioactive reactions follows first order kinetics.

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

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

We are given:

$t_{1/2}=1hr$

Putting values in above equation, we get:

$k=\frac{0.693}{1}=0.693hr^{-1}$

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 = $0.693hr^{-1}$

t = time taken for decay process = 3.00 pm - 12.00 pm = 3 hour

$[A_o]$ = initial amount of the reactant = 20 g

[A] = amount left after decay process =  ?

Putting values in above equation, we get:

$0.693hr^{-1}=\frac{2.303}{3hr}\log\frac{20}{[A]}$

$[A]=2.5g$

Hence, the correct answer is Option c.

Answer 2

your answer should be C.

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