Question:
The half life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be
The half life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be
Updated On: May 3, 2024
- 150 years
- 200 years
- 250 years
- 100 years
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The Correct Option is B
Solution and Explanation
$X \rightarrow Y$
$X : Y =1: 15$
A.P. $=\frac{1}{16}=\frac{1}{2^{ n }}$
No. of half life $n =4$
$t = n T _{1 / 2}=4 \times 50=200 \,yr$
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Concepts Used:
Nuclei
In the year 1911, Rutherford discovered the atomic nucleus along with his associates. It is already known that every atom is manufactured of positive charge and mass in the form of a nucleus that is concentrated at the center of the atom. More than 99.9% of the mass of an atom is located in the nucleus. Additionally, the size of the atom is of the order of 10-10 m and that of the nucleus is of the order of 10-15 m.
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Following are the terms related to nucleus:
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- Mass Number
- Nuclear Size
- Nuclear Density
- Atomic Mass Unit