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

$A$ $280\, \text{day}$ old radioactive substance shows an activity of $6000\, \text{dps}$. $140\, \text{days}$ later, its activity becomes $3000\, \text{dps}$. What was its initial activity? ......... $\text{dps}$

The half-life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be:

During the mean life of a radioactive element,the fraction that disintegrates is

Define the decay constant and state its $SI$ unit.

$A$ radioactive sample is undergoing $\alpha$ decay. At any time $t_{1}$,its activity is $A$ and at another time $t_{2}$,the activity is $\frac{A}{5}$. What is the average life time for the sample?

Vedclass Test Series

Exam Paper Generator

Online Exam Module