JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Chemical Kinetics

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A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min and that of B is 5 min. If the initial concentration of B is 4 times that of A and they both start decaying at the same time, how much time will it take for the concentration of both of them to be same? ____ min.

Answer: 15

Solution

Writing each amount through its half-life,

N_{A} = N_{0} (\frac{1}{2})^{t /15}

with

N_{0}

the initial amount of A, while B starts at four times this,

N_{B} = 4 N_{0} (\frac{1}{2})^{t /5}

. Setting the two equal and cancelling

N_{0}

gives

(\frac{1}{2})^{t /15} = 4 (\frac{1}{2})^{t /5} = (\frac{1}{2})^{t /5 - 2}

. Equating the exponents,

\frac{t}{15} = \frac{t}{5} - 2

, which rearranges to

\frac{2 t}{15} = 2

. The two concentrations become equal after 15 minutes.

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Integer answer

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JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Chemical Kinetics

Solution

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