If N0 is the original mass of the substance of half life \(t_{\frac{1}{2}}=4\) years, then the amount of substance left after 12 years is :

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CUET Physics 18th Aug 2022 Official Paper
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  1. N0/16
  2. N0/4
  3. N0/8
  4. N0/2

Answer (Detailed Solution Below)

Option 3 : N0/8
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Detailed Solution

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Calculation:

The amount of substance left after 12 years can be found using the formula for radioactive decay:

N(t) = No * (1/2)​(t/t1/2)

where N(t) is the amount of substance remaining after time t, No is the original amount of substance, t1/2 is the half-life, and t is the time elapsed.

In this case, No (since No is the original mass), t1/2 = 4 years, and t = 12 years.

Substituting these values into the formula gives:

N(12) = No * (1/2)12/4
N(12) = No * (1/2)3
N(12) = No/8
N(12) = 0.125 * No

Therefore, after 12 years, the amount of substance remaining is 0.125 times the original mass or 12.5% of the original mass.

N = N0/8

The correct answer is option (3)

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