A radioactive element will decay by 99% betwe | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The amount of radioactive substance remaining after $n$ half-lives is given by $N = N_0 \left( \frac{1}{2} \right)^n$.If $99\%$ of the element dec

Vedclass · Accepted Answer

$6$ and $7$ half-lives

Vedclass · Answer

(A) The amount of radioactive substance remaining after $n$ half-lives is given by $N = N_0 \left( \frac{1}{2} \right)^n$.If $99\%$ of the element decays,the amount remaining is $N = N_0 - 0.99 N_0 = 0.01 N_0$.Substituting this into the equation: $0.01 N_0 = N_0 \left( \frac{1}{2} \right)^n$.$\frac{1}{100} = \left( \frac{1}{2} \right)^n$.Taking the reciprocal: $100 = 2^n$.We know that $2^6 = 64$ and $2^7 = 128$.Since $64 < 100 < 128$,the value of $n$ must lie between $6$ and $7$ half-lives.

$A$ radioactive element will decay by $99\%$ between which of the following number of half-lives?

Similar Questions

The half-life of a radioactive element which has only $\frac{1}{32}$ of its original mass left after a lapse of $60\, days$ is ........ $days$.

The specific activity of $Ra^{226}$ is $1 \, Ci/g$. The activity of $1 \, \mu g$ of $Ra^{226}$ will be:

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5 \, minutes$. The time (in $minutes$) at which the activity reduces to half its value is

Two different radioactive elements with half-lives $T_1$ and $T_2$ have undecayed atoms $N_1$ and $N_2$ respectively present at a given instant. The ratio of their activities at that instant is

$A$ radioactive sample has a half-life of $5$ years. The percentage of the fraction decayed in $10$ years will be (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module