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

The half-life of a radionuclide is $69.3 \text{ minutes}$. What is its average life (in minutes)?

The half-life of a radioisotope is $20 \ hours$. After $60 \ hours$,what fraction of the initial amount will remain?

The half-life of a radioisotope is $4 \ hours$. If the initial mass of the isotope is $200 \ g$,then the mass remaining after $24 \ hours$ will be ....... $g$.

$A$ freshly prepared radioactive source of half-life $2 \ hours$ emits radiations of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with this source is ......... $hours$.

The rate of radioactive disintegration at an instant for a radioactive sample of half-life $2.2 \times 10^{9} \ s$ is $10^{10} \ s^{-1}$. The number of radioactive atoms in that sample at that instant is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module