Question

plzz help me frnds
who will answer correctly they will be marked as brainliest..

Answer 1

As this is a competitive exam question, let us solve it with minimum working.

Half life is the amount of time required for a substance to decay to one-half of its original weight. Thus, if 1g of a substance undergoes disintegration equivalent to 1 half life, 0.5 g will disintegrate and 0.5 g will remain.

We see that both the nuclides disintegrate for 4 minutes. The half-life of A is 1 minute, hence it undergoes disintegration equivalent to 4 half lives.
In one half life, $\frac{1}{2}$ of the substance remains. So, after 4 half lives, $( \frac{1}{2} ) ^{4}$ will remain, i.e. $\frac{1}{16}$ will remain. Hence, we can say 1 - $\frac{1}{16}$  = $\frac{15}{16}$ of the element has disintegrated.

Coming to nuclide B, it has a half-life of 2 minutes. Thus, it undergoes a disintegration equivalent to 2 half lives. In 2 half lives, $( \frac{1}{2} ) ^{2}$ = $\frac{1}{4}$ of the element will remain. Thus, 1 -  $\frac{1}{4}$  =  $\frac{3}{4}$ would have disintegrated.

Taking the ratio of the weights of A and B disintegrated, we have
$\frac{15}{16}$ : $\frac{3}{4}$
Canceling the denominators and numerators, we have
$\frac{5}{4}$ : $\frac{1}{1}$
Multiplying each side by 4, we have
$\frac{5}{4}$ * 4 :  $\frac{1}{1}$ * 4
= 5 : 4

Thus, option (2), i.e., 5:4 is the correct answer.

Answer 2

As this is a competitive exam question, let us solve it with minimum working.

Half life is the amount of time required for a substance to decay to one-half of its original weight. Thus, if 1g of a substance undergoes disintegration equivalent to 1 half life, 0.5 g will disintegrate and 0.5 g will remain.

We see that both the nuclides disintegrate for 4 minutes. The half-life of A is 1 minute, hence it undergoes disintegration equivalent to 4 half lives.
In one half life, of the substance remains. So, after 4 half lives, will remain, i.e.  will remain. Hence, we can say 1 -   = of the element has disintegrated.

Coming to nuclide B, it has a half-life of 2 minutes. Thus, it undergoes a disintegration equivalent to 2 half lives. In 2 half lives,  =  of the element will remain. Thus, 1 -    =   would have disintegrated.

Taking the ratio of the weights of A and B disintegrated, we have
:
Canceling the denominators and numerators, we have
:
Multiplying each side by 4, we have
* 4 :   * 4
= 5 : 4

Thus, option (2), i.e., 5:4 is the correct answer.

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