# Two radioactive elements A and B have half-lives of 100 and 50 years respectively....

Question 52
A
4 : 1
B
2 : 1
C
1 : 1
D
1 : 2
E
1 : 4
##### Explanation

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

=$$4 : 16$$ = $$1 : 4$$

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