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Two radioactive elements A and B have half-lives of 100 a...

Two radioactive elements A and B have half-lives of 100 and 50 years respectively. Samples of A and B initially contain equal amounts/number of atoms. What is the ratio of the number of the remaining atoms of A to that of B after 200 years?

A.

4 : 1

B.

2 : 1

C.

1 : 1

D.

1 : 2

E.

1 : 4

Correct answer is A

Given that a mass N of elements A and B exists, then:

For element A, after 100 years, we have A of mass N/2 remaining

After 200 years, we have A of mass \(\frac{1}{2}\times\frac{N}{2}\) = \(\frac{N}{4}\)

For element B, after 50 years, we have B of mass N/2 remaining

After 100 years, we have B of mass \(\frac{1}{2}\times\frac{N}{2}\) = \(\frac{N}{4}\)

After 150 years, we have B of mass \(\frac{1}{2}\times\frac{N}{4}\) = \(\frac{N}{8}\)

After 200 years,we have B of mass \(\frac{1}{2}\times\frac{N}{8}\) = \(\frac{N}{16}\)

Ratio: \((\frac{N}{4} : \frac{N}{16})\) 

=\(4 : 16\)  = \(1 : 4\)