Question: Half life of an element is 16 hours. What time will it take for 75% disintegration? (A) 32 days ...

Question

Half life of an element is 16 hours. What time will it take for 75% disintegration?
(A) 32 days
(B) 32 hours
(C) 48 hours
(D) 16 hours

Answer 1

Solution

Hint : To answer this question, we need to understand the concept of half-life and the property of decay of radioactive elements. Radioactive elements exhibit the property of decaying over time. As a result, the concentration of the substance decreases over time.

Complete Step By Step Answer:
The half-life of a chemical reaction is the time it takes for a particular reactant's concentration to reach 50% of its initial concentration (i.e. the time taken for the reactant concentration to reach half of its initial value). It is commonly represented in seconds and is indicated by the sign ${t_{\dfrac{1}{2}}}$ .
It is to be noted that the formula for a reaction's half-life varies depending on the reaction's order.
The half-life of a zero-order reaction can be calculated using the mathematical calculation ${t_{\dfrac{1}{2}}} = \dfrac{{{{[R]}_o}}}{{2k}}$
The half-life of a first-order reaction is calculated as ${t_{\dfrac{1}{2}}} = \dfrac{{0.693}}{{2k}}$
The half-life of a second-order reaction is calculated using the formula $\dfrac{1}{{k{{[R]}_o}}}$ .
Here, ${[R]_o}$ is the initial reactant concentration.
$k$ is the constant of reaction.
Now we know that 75% decay takes place in $\dfrac{3}{4}th$ life.
So, time taken can be calculated as:
Elements will disintegrate by 50% in the first half of life.
In the next half life, elements will again disintegrate by 50%.
Thus, in total two half lives, elements will disintegrate by 75%.
So time taken = 2 x 16 = 32 hours.
So, option (a) is correct.

Note :
The nucleus of an unstable atom loses energy through producing radiation, which is known as radioactivity. A little amount of Uranium compound was wrapped in black paper and put in a drawer containing photographic plates. After further examination of these plates, it was discovered that there had been an exposure. The term "radioactive decay" was used to describe this occurrence.