Which one of the following statement is true , if half - life of a radioactive substance is 1 month ?

Options

A. A)`7//8^(th)` part of the substance will disintegrate in 3 months
B. B)`1//8^(th)` part of the substance will remain undecayed at the end of 4 months
C. C)The substance will disintegrate completely in 4 months
D. D)`1//16^(th)` part of the substance will remain undecayed at the end of 3 months

Answer

A

Explanation

`(N)/(N_(0))=((1)/(2))^(n)or(N)/(N_(0))=((1)/(2))^(t//t_(1)//2)` or
`(N)/(N_(0))=((1)/(2))^(t//1)` For t= 3 months
`(N)/(N_(0))=((1)/(2))^(3)=(1)/(8)` Therefore , disintegrated part substance in 3 months
`=1-(1)/(8)=(7)/(8)`.