Ram was a daily wage worker in a factory. He was suffering from Cancer. On hearing this, most of his co-workers, started avoiding him under the impression that it was a contagious disease. When Prof. Srivastava came to know about this, case, he took him to a leading radiologist, who examined him and told that it was at the beginning stage. He advised that it could be easily cured and also certified that it was not a communicable disease. After this, Ram was given proper treatment by the doctor and got cured completely.
(1) What moral values did Prof. Srivastava display ?
(2) How is mean life of a radioactive element related to its half life?
(3) A radioactive sample has activity of 10,000 disintegrations per second after 20 hours . After next 10 hours, its activity reduces to 5,000 dps. Find out its half - life and initial activity.

Explanation

(1) Awareness and Humanity.
(2)`t_(1//2)=(0.6931)/lambda and tau = 1//lambda`
`(T/(1//2))/tau=0.6931 and T_(1//2)=0.6931 tau`
(3)` R_(0)=10,000s^(-1) R= 5000 s^(-1) t= 10h`
` = 5000/10000 = e^(-10 lambda) rArr e^(-10) lambda=2`
taking ` log 10 lambda = log2 rArr 10 lambda = 2.303 xx log _(10^(2)) lambda = (0.6931)/10 per h`
`T_(1//2) = (0.6931)/lambda =cancel(6931)/cancel (6931) xx 10 h = 10h`
Intial activity = `A _(0)`
Using `5000=R_(0)(e^(-0.693))/(36 xx 10^(3)) xx 30 xx 60 xx 60 rArr 5000 = A_(0) e^(-.693 xx3)`
`A_(0) = 5 xx 10^(3) xx e^(0.693 xx 3) ` decay/sec.