MCQ Detailed View

Radioactivity is the process by which unstable atomic nuclei lose energy by emitting radiation. The half-life of a radioactive element is the time required for half of its atoms or mass to decay. This is a fixed property of each radioactive substance and does not depend on temperature, pressure, or the amount of material present.

In this problem, the substance starts with a mass of 10 mg and we want to know how long it will take to reduce to 5 mg. By definition, half-life is the time required to reduce the original amount by 50%. Since the half-life given is 8 days, and 5 mg is exactly half of 10 mg, it will take one half-life, or 8 days, for the mass to decrease from 10 mg to 5 mg.

If we were to reduce it further, say to 2.5 mg, another 8 days (a second half-life) would be needed, making it 16 days in total. The decay follows an exponential law:

N=N0×(12)t/TN = N_0 \times \left(\frac{1}{2}\right)^{t/T}N=N0×(21)t/T

Where:

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  N0N_0N0 = initial amount

  
  


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  $N$ = remaining amount

  
  


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  $T$ = half-life

  
  


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  $t$ = time

  
  

Here,
$10\to 5$ means N=N0/2N = N_0/2N=N0/2, so $t=T=8$ days.

Reviewing the options:

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  4 days: Too short, only half a half-life.

  
  


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  12 days: Does not match one half-life.

  
  


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  16 days: Two half-lives would reduce to 2.5 mg, not 5 mg.

  
  


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  8 days: ✅ Correct.

  
  


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  None of these: Incorrect.

  
  

Thus, the correct answer is 8 days, showing the predictable pattern of radioactive decay described by half-life.