The half-life of a radioactive substance is 2 | vedclass

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

Question

(B) The decay constant $\lambda$ is given by $\lambda = \frac{\ln(2)}{T_{1/2}} = \frac{0.693}{20} \approx 0.03465 \ min^{-1}$.The time $t$ required fo

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) The decay constant $\lambda$ is given by $\lambda = \frac{\ln(2)}{T_{1/2}} = \frac{0.693}{20} \approx 0.03465 \ min^{-1}$.The time $t$ required for a substance to decay is given by $t = \frac{1}{\lambda} \ln \left( \frac{N_0}{N} ight)$.For $33\%$ disintegration,the remaining amount $N_1 = N_0 - 0.33N_0 = 0.67N_0$. The time $t_1$ is:$t_1 = \frac{1}{0.03465} \ln \left( \frac{1}{0.67} ight) \approx 28.95 	imes 0.4005 \approx 11.6 \ min$.For $67\%$ disintegration,the remaining amount $N_2 = N_0 - 0.67N_0 = 0.33N_0$. The time $t_2$ is:$t_2 = \frac{1}{0.03465} \ln \left( \frac{1}{0.33} ight) \approx 28.95 	imes 1.1087 \approx 32.1 \ min$.The time difference is $\Delta t = t_2 - t_1 = 32.1 - 11.6 = 20.5 \ min$.Rounding to the nearest integer,the difference is approximately $20 \ min$.

The half-life of a radioactive substance is $20$ minutes. The difference between the points of time when it is $33\%$ disintegrated and $67\%$ disintegrated is approximately ......... $min$.

Similar Questions

$A$ radioactive element has a rate of disintegration $10,000$ disintegrations per minute at a particular instant. After four minutes it becomes $2500$ disintegrations per minute. The decay constant per minute is (in $log _e 2$)

After $280$ days,the activity of a radioactive sample is $6000 \, dps$. The activity reduces to $3000 \, dps$ after another $140$ days. The initial activity of the sample in $dps$ is

The atomic weight of a radioactive element is $M_w$ grams. The radioactivity of $m$ grams of this element is ......... ($N_A$ is Avogadro's number,$\lambda$ is the decay constant).

The half-life period of element $X$ is same as the mean life time of element $Y$. Assume initially $X$ and $Y$ have same number of atoms. Then

Consider two nuclei of the same radioactive nuclide. One of the nuclei was created in a supernova explosion $5$ billion years ago. The other was created in a nuclear reactor $5$ minutes ago. The probability of decay during the next time interval is

Vedclass Test Series

Exam Paper Generator

Online Exam Module