Question:
Half life of radioactive element is 12.5 Hour and its quantity is 256 gm. After how much time its quantity will remain 1 gm : -
Half life of radioactive element is 12.5 Hour and its quantity is 256 gm. After how much time its quantity will remain 1 gm : -
Updated On: Jul 4, 2024
- 50 Hrs
- 100 Hrs
- 150 Hrs
- 200 Hrs
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The Correct Option is B
Solution and Explanation
The mass of radioactive substance remained is, $M={{M}_{0}}{{\left( \frac{1}{2} \right)}^{n}}$
Here, $M=1\,g,\,\,{{M}_{0}}=256\,g,\,{{t}_{1/2}}=12.5\,h$
$So,1=256\,{{\left( \frac{1}{2} \right)}^{n}}$
OR $\frac{1}{256}={{\left( \frac{1}{2} \right)}^{n}}$
OR ${{\left( \frac{1}{2} \right)}^{8}}={{\left( \frac{1}{2} \right)}^{N}}$
Comparing the powers on both the sides, we get
$n=8=\frac{t}{{{T}_{1/2}}}$
$\therefore t=8{{T}_{1/2}}=8\times 12.5=100\,h$
Here, $M=1\,g,\,\,{{M}_{0}}=256\,g,\,{{t}_{1/2}}=12.5\,h$
$So,1=256\,{{\left( \frac{1}{2} \right)}^{n}}$
OR $\frac{1}{256}={{\left( \frac{1}{2} \right)}^{n}}$
OR ${{\left( \frac{1}{2} \right)}^{8}}={{\left( \frac{1}{2} \right)}^{N}}$
Comparing the powers on both the sides, we get
$n=8=\frac{t}{{{T}_{1/2}}}$
$\therefore t=8{{T}_{1/2}}=8\times 12.5=100\,h$
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Concepts Used:
Decay Rate
The disintegration of unstable heavy atomic nuclei into lighter, more stable, atomic nuclei, accompanied in the process by the emission of ionizing radiation (alpha particles, beta particles or gamma rays). This is a random process at the atomic level but, given a large number of similar atoms, the decay rate on average is predictable, and is usually measured by the half-life of the substance.
The equation for finding out the decay rate is given below:
