If 10% of a radioactive material decays in 5 | vedclass

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

Question

(B) The radioactive decay law is given by $N(t) = N_0 e^{-\lambda t}$.After $t = 5$ days,$10\%$ decays,so $90\%$ remains: $0.9 N_0 = N_0 e^{-5\lambda}

Vedclass · Accepted Answer

$65$

Vedclass · Answer

(B) The radioactive decay law is given by $N(t) = N_0 e^{-\lambda t}$.After $t = 5$ days,$10\%$ decays,so $90\%$ remains: $0.9 N_0 = N_0 e^{-5\lambda}$.Taking the natural logarithm on both sides: $5\lambda = -\ln(0.9) = \ln(1/0.9) = \ln(1.111) \approx 0.10536$.So,$\lambda = 0.02107 	ext{ days}^{-1}$.After $t = 20$ days,the remaining amount $N$ is $N = N_0 e^{-\lambda(20)}$.$N = N_0 e^{-(0.02107 	imes 20)} = N_0 e^{-0.4214}$.$N \approx N_0 	imes 0.656$.Thus,approximately $65.6\%$ of the material remains,which is closest to $65\%$.

If $10\%$ of a radioactive material decays in $5$ days,then the amount of original material left after $20$ days is approximately ...............$\%$

Similar Questions

The reagent used in the preparation of aspirin from salicylic acid is

In the visible region,the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega, \omega'$ and $d, d'$ respectively. The condition for getting deviation without dispersion when the two prisms are combined is

In a biprism experiment,if the $5^{\text{th}}$ bright band with wavelength $\lambda_{1}$ coincides with the $6^{\text{th}}$ dark band with wavelength $\lambda_{2}$,then the ratio $\left(\frac{\lambda_{2}}{\lambda_{1}}\right)$ is:

Which of the following organisms belongs to the Kingdom $Monera$?

$A$ spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown. The electric field inside the emptied space is

Vedclass Test Series

Exam Paper Generator

Online Exam Module