The decay constants of a radioactive substanc | vedclass

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

Question

(C) When a radioactive substance decays through multiple processes simultaneously,the total decay constant is the sum of the individual decay constant

Vedclass · Accepted Answer

$\frac{T_{\alpha}T_{\beta}}{T_{\alpha} + T_{\beta}}$

Vedclass · Answer

(C) When a radioactive substance decays through multiple processes simultaneously,the total decay constant is the sum of the individual decay constants.Thus,the effective decay constant is $\lambda_{eff} = \lambda_{\alpha} + \lambda_{\beta}$.The half-life $T$ is related to the decay constant $\lambda$ by $T = \frac{\ln 2}{\lambda}$,which implies $\lambda = \frac{\ln 2}{T}$.Substituting this into the effective decay constant equation:$\frac{\ln 2}{T_{eff}} = \frac{\ln 2}{T_{\alpha}} + \frac{\ln 2}{T_{\beta}}$.Dividing by $\ln 2$ on both sides,we get $\frac{1}{T_{eff}} = \frac{1}{T_{\alpha}} + \frac{1}{T_{\beta}}$.Solving for $T_{eff}$,we obtain $T_{eff} = \frac{T_{\alpha}T_{\beta}}{T_{\alpha} + T_{\beta}}$.

The decay constants of a radioactive substance for $\alpha$ and $\beta$ emission are $\lambda_{\alpha}$ and $\lambda_{\beta}$ respectively. If the substance emits $\alpha$ and $\beta$ simultaneously,then the average half-life of the material will be:

Similar Questions

Ten percent of a radioactive sample has decayed in $1$ day. After $2$ days,the decayed percentage of nuclei will be ...... $\%$

The decay constant of a radioactive element is $0.01 \ s^{-1}$. Its half-life period is ....... $s$.

The radioactivity of a certain radioactive element drops to $1/64$ of its initial value in $30 \, s$. Its half-life is ......... $s$.

The graph represents the decay of a newly prepared sample of radioactive nuclide $X$ to a stable nuclide $Y$. The half-life of $X$ is $\tau$. The growth curve for $Y$ intersects the decay curve for $X$ after time $T$. What is the time $T$?

The half-life of a neutron is $693 \ s$. What fraction of neutrons will decay when a beam of neutrons, having kinetic energy of $0.084 \ eV$, travels a distance of $1 \ km$? (mass of neutron $= 1.68 \times 10^{-27} \ kg$, and $\ln 2 = 0.693$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module