Question

Nuclear decay occurs according to first-order kinetics. How long will it take for a sample of radon-218 to decay from 99 g to 0.50 g? The half-life of radon-218 is 35 milliseconds.

a. 2.6 x 102 ms.
b. 2.0 10 ms.
c. 1.1 x 10 ms.
d. 6.6 x 102 ms.

Answer 1

a. 2.6 x 102 ms

Step-by-step explanation:

Initial mass [Ao] = 99 g

Final mass [A] = 0.50 g

Half life (t1/2) = 35 ms

Time ( t ) = ?

]The integrated rate law for first order reactions is given as;

To obtain k, we look at the expression for the half life of a first order reaction;

t1/2 = 0.693 / k

k = 0.693 / 35 = 0.0198 ms-1

ln[A] = ln[Ao] - kt

kt = ln[Ao] - ln[A]

t = ( ln[Ao] - ln[A] ) / k

t = ( ln(99) - ln (0.50) ) / 0.0198

t = 5.288 / 0.0198

t = 267.07 ms

correct option is;

a. 2.6 x 102 ms