Question

A sample has passed through 6 half-lives, what is the ratio of parent isotopes to daughter isotopes?

A. 1 parent isotope for every 6 daughter isotopes
B. 6 parent isotopes for every 1 daughter isotopes
C. 1 parent isotope for every 64 daughter isotopes
D. 1 parent isotope for every 63 daughter isotopes

Answer 1

The answer is A. 1 parent isotope for every 6 daughter isotope.

Why? Because One half-life after a radioactive isotope is incorporated intoa rock there will be only half of the original radioactive parent atoms remaining and an equal number of daughter atoms will have been produced. The ratio of parent to daughter after on half-life will be 1:1. After two half-lives, half of the remaining half will decay, leaving one quarter of the original radioactive parent atoms. Those transformed atoms bring the tally of daughter atoms to three-quarters of the crop of parent plus daughter atoms. The ratio of parent to daughter atoms after two half-lives is therefore 1:3 (one-quarter to three quarters).  So there you have it a ratio of 1:6.

Answer 2

Answer:

Option C

Explanation:

After energy half life, a radioactive substance reduces its weight by half

After first half life, weight of the sample would be $\frac{W}{2}$

After second half life, weight of the sample would be $\frac{W}{4}$

After third half life, weight of the sample would be $\frac{W}{8}$

After fourth half life, weight of the sample would be $\frac{W}{16}$

After fifth half life, weight of the sample would be $\frac{W}{32}$

After sixth half life, weight of the sample would be $\frac{W}{64}$

Hence Option C is correct