Question

A radioactive substance has a half life of four months, Three fourth of the substance will decay in
A Three months
B Four months
C Eight month
D Twelve months

Answer 1

Hint :- Half life of any radioactive substance is the amount of time required for the quantity by weight of the substance to fall to half its initial value. So after one half life , we will have $\dfrac{1}{2}$ or 50% of the substance remaining. And after 2 half lives , we will have $\dfrac{1}{4}$ of the substance remaining. In other words, ¾ of the substance will take two half lives to decay

Complete step by step solution
Let the Amount of Radioactive Substance in initial time be R
Since it is Given that the Half Life of the Radioactive Substance is 4 Months
so after four month The Amount of Radioactive Substance would Decay by $\dfrac{R}{2}$
and after eight months the amount of radioactive substance would decay by
$\dfrac{R}{2} + \dfrac{R}{4}$
After solving above equation
$\dfrac{R}{2} + \dfrac{R}{4} = \dfrac{{3R}}{4}$
As one half life is given as 4 months , so the substance will take 8 months to decay by $\raise.5ex\hbox{$\scriptstyle 3$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 3$}$ the quantity by weight so, Three Fourth of the Radioactive Substance would decay in 8 Months

Option C is correct

Note- Half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive