The half-life of a radioactive element is 10 | vedclass

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

Question

(B) Radioactive decay follows first-order kinetics. The decay constant $k = \frac{0.693}{t_{1/2}} = \frac{0.693}{10} \ h^{-1}$.Using the first-order i

Vedclass · Accepted Answer

$4.56 	imes 10^{23} \ 	ext{atoms}$

Vedclass · Answer

(B) Radioactive decay follows first-order kinetics. The decay constant $k = \frac{0.693}{t_{1/2}} = \frac{0.693}{10} \ h^{-1}$.Using the first-order integrated rate equation: $k = \frac{2.303}{t} \log \frac{N_0}{N_t}$.Given $N_0 = 1 \ g$-atom,$t = 4 \ h$,and $k = 0.0693 \ h^{-1}$.$0.0693 = \frac{2.303}{4} \log \frac{1}{N_t} \implies \log \frac{1}{N_t} = \frac{0.0693 	imes 4}{2.303} \approx 0.12036$.$\log N_t = -0.12036 = \bar{1}.87964 \implies N_t = 10^{-0.12036} \approx 0.7579 \ g$-atoms.Number of atoms $= N_t 	imes N_A = 0.7579 	imes 6.022 	imes 10^{23} \approx 4.56 	imes 10^{23} \ 	ext{atoms}$.

The half-life of a radioactive element is $10 \ hours$. How much will be left after $4 \ hours$ in a $1 \ g$-atom sample?

Similar Questions

$A$ radioactive element with half-life $6.5 \ hr$ has $48 \times 10^{19}$ atoms. Number of atoms left after $26 \ hr$ is:

$A$ radioactive isotope has a half-life of $20 \ days$. If $100 \ g$ of the substance is taken,the weight of the isotope remaining after $40 \ days$ is ......... $g$.

What is the half-life (in $\text{min}$) of a radioactive substance if $75\%$ of a given amount of the substance disintegrates in $30 \, \text{min}$?

$A$ certain nuclide has a half-life of $25 \ min$. If one starts with $100 \ g$ of it,how much of it will remain at the end of $100 \ min$?

$A$ sample of rock from the moon contains an equal number of atoms of uranium and lead ($t_{1/2}$ for $U = 4.5 \times 10^9$ years). The age of the rock would be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module