Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half lives 1 month and 2 months respectively. At time $t=$ 0 , number of nuclei of each $P$ and $Q$ is $x$. Time at which rate of disintegration of $P$ and $Q$ are equal, number of nuclei of $R$ is ........ $x$
Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half lives 1 month and 2 months respectively. At time $t=$ 0 , number of nuclei of each $P$ and $Q$ is $x$. Time at which rate of disintegration of $P$ and $Q$ are equal, number of nuclei of $R$ is ........ $x$
- A
$1$
- B
$1.25$
- C
$1.5$
- D
$1.75$
Similar Questions
Following statements related to radioactivity are given below
$(A)$ Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
$(B)$ The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
$(C)$ Slope of the graph of $\log _{e}$ (no. of undecayed nuclei) $Vs$. time represents the reciprocal of mean life time $(\tau)$.
$(D)$ Product of decay constant ( $\lambda$ ) and half-life time $\left(T_{1 / 2}\right)$ is not constant.
Choose the most appropriate answer from the options given below
Following statements related to radioactivity are given below
$(A)$ Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
$(B)$ The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
$(C)$ Slope of the graph of $\log _{e}$ (no. of undecayed nuclei) $Vs$. time represents the reciprocal of mean life time $(\tau)$.
$(D)$ Product of decay constant ( $\lambda$ ) and half-life time $\left(T_{1 / 2}\right)$ is not constant.
Choose the most appropriate answer from the options given below
- [JEE MAIN 2022]
A radioactive nucleus decays by two different process. The half life of the first process is $5$ minutes and that of the second process is $30\,s$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11}\,s$. The value of $\alpha$ is $..............$
A radioactive nucleus decays by two different process. The half life of the first process is $5$ minutes and that of the second process is $30\,s$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11}\,s$. The value of $\alpha$ is $..............$
- [JEE MAIN 2023]
The normal activity of living carbon-containing matter is found to be about $15$ decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive $_{6}^{14} C$ present with the stable carbon isotope $_{6}^{12} C$. When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life ($5730$ years) of $_{6}^{14} C ,$ and the measured activity, the age of the specimen can be approximately estimated. This is the principle of $_{6}^{14} C$ dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of $9$ decays per minute per gram of carbon. Estimate the approximate age (in $years$) of the Indus-Valley civilisation
The normal activity of living carbon-containing matter is found to be about $15$ decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive $_{6}^{14} C$ present with the stable carbon isotope $_{6}^{12} C$. When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life ($5730$ years) of $_{6}^{14} C ,$ and the measured activity, the age of the specimen can be approximately estimated. This is the principle of $_{6}^{14} C$ dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of $9$ decays per minute per gram of carbon. Estimate the approximate age (in $years$) of the Indus-Valley civilisation
$1 \,mg$ gold undergoes decay with $2.7$ days half-life period, amount left after $8.1$ days is ......... $mg$
$1 \,mg$ gold undergoes decay with $2.7$ days half-life period, amount left after $8.1$ days is ......... $mg$
The half-life of $^{215}At$ is $100\mu s$. The time taken for the radioactivity of a sample of $^{215}At$ to decay to $\frac{{1}}{{16}} \,th$ of its initial value is .........$\mu s$
The half-life of $^{215}At$ is $100\mu s$. The time taken for the radioactivity of a sample of $^{215}At$ to decay to $\frac{{1}}{{16}} \,th$ of its initial value is .........$\mu s$
- [IIT 2002]