A radioactive element gets spilled over the f | vedclass

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

Question

(A) The radioactive decay follows first-order kinetics,where the activity $A$ at time $t$ is given by $A = A_0 e^{-\lambda t}$.Given that the initial

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(A) The radioactive decay follows first-order kinetics,where the activity $A$ at time $t$ is given by $A = A_0 e^{-\lambda t}$.Given that the initial activity $A_0 = 10A$,where $A$ is the permissible safe activity level.The decay constant $\lambda$ is related to the half-life $t_{1/2}$ by $\lambda = \frac{\ln 2}{t_{1/2}} = \frac{0.693}{30 	ext{ days}}$.Using the first-order integrated rate equation: $t = \frac{2.303}{\lambda} \log_{10} \left( \frac{A_0}{A} ight)$.Substituting the values: $t = \frac{2.303}{(0.693 / 30)} \log_{10} (10)$.Since $\frac{2.303}{0.693} \approx \frac{1}{0.434} \approx 3.32$ (or more precisely $\frac{2.303}{0.693} \approx 3.32$ and $3.32 	imes 30 \approx 100$),we get $t = 30 	imes \frac{2.303}{0.693} 	imes 1 = 30 	imes 3.325 \approx 100 	ext{ days}$.

$A$ radioactive element gets spilled over the floor of a room. Its half-life period is $30$ days. If the initial activity is ten times the permissible value,after how many days will it be safe to enter the room?

Similar Questions

$8 \, g$ of the radioactive isotope,cesium$-137$ were collected on February $1$ and kept in a sealed tube. On July $1$,it was found that only $0.25 \, g$ of it remained. So the half-life period of the isotope is ....... $days$.

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

The half-life of a radioactive isotope is $3 \ hours$. If the initial mass of the isotope is $256 \ g$,how much mass in $g$ will remain after $18 \ hours$ (in $.0$)?

$A$ 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:

Decay of $_{92}U^{235}$ is $...$ order reaction.

Vedclass Test Series

Exam Paper Generator

Online Exam Module