SATHEE: Atoms And Nuclei Question 364

Atoms And Nuclei Question 364

Question: At radioactive equilibrium, the ratio between the atoms of two radioactive elements (X) and (Y) as found to be $3.2 \times 10^{9} : 1$ respectively If half-life of the element is $1.6 \times 10^{10}$ years, then half-life of the element W would be

Options:

A) $3.2 \times 10^{9} y e a r s$

B) $5 \times 10^{9} y e a r s$

C) $1.6 \times 10^{10} y e a r s$

D) 5 years

Show Answer

Answer:

Correct Answer: D

Solution:

$X \overset{λ_{1}}{\to} Y \overset{λ_{2}}{\to} Z$

At radioactive equilibrium, $(λ_{X}) \times (N_{X}) = (λ_{Y}) \times (N_{Y})$

$\frac{λ_{X}}{λ_{Y}} = \frac{N_{Y}}{N_{X}} \frac{{(t_{1 / 2})}_{Y}}{{(t_{1 / 2})}_{X}} = \frac{N_{Y}}{N_{X}}$ or $\frac{{(t_{1 / 2})}_{Y}}{1.6 \times 10^{10}}$ $= \frac{1}{3.2 \times 10^{9}} {(t_{1 / 2})}_{Y} = 5 y e a r s$

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Atoms And Nuclei Question 364

Question: At radioactive equilibrium, the ratio between the atoms of two radioactive elements (X) and (Y) as found to be 3.2×109:1 respectively If half-life of the element is 1.6×1010 years, then half-life of the element W would be

Options:

Answer:

Solution:

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Question: At radioactive equilibrium, the ratio between the atoms of two radioactive elements (X) and (Y) as found to be $3.2 \times 10^{9} : 1$ respectively If half-life of the element is $1.6 \times 10^{10}$ years, then half-life of the element W would be