Physics Discuss

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

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

=\(4 : 16\) = \(1 : 4\)


Correct option: A
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