Nuclear Physics JEE Main PYQs, 2020 to 2025

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

A radioactive nucleus $\mathrm{n}_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$, after one half-life of $n_1$ ?

A star has $100 \%$ helium composition. It starts to convert three ${ }^4 \mathrm{He}$ into one ${ }^{12} \mathrm{C}$ via triple alpha process as $${ }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\mathrm{Q}$$. The mass of the star is $2.0 \times 10^{32} \mathrm{~kg}$ and it generates energy at the rate of $5.808 \times 10^{30} \mathrm{~W}$. The rate of converting these ${ }^4 \mathrm{He}$ to ${ }^{12} \mathrm{C}$ is $\mathrm{n} \times 10^{42} \mathrm{~s}^{-1}$, where $\mathrm{n}$ is _________. [ Take, mass of ${ }^4 \mathrm{He}=4.0026 \mathrm{u}$, mass of ${ }^{12} \mathrm{C}=12 \mathrm{u}$]

In a hypothetical fission reaction

${ }_{92} X^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} Z^{92}+3 R$

The identity of emitted particles (R) is :

A common example of alpha decay is $${ }_{92}^{238} \mathrm{U} \longrightarrow{ }_{90}^{234} \mathrm{Th}+{ }_{2} \mathrm{He}^{4}+\mathrm{Q}$$

Given :

${ }_{92}^{238} \mathrm{U}=238.05060 ~\mathrm{u}$,

${ }_{90}^{234} \mathrm{Th}=234.04360 ~\mathrm{u}$,

${ }_{2}^{4} \mathrm{He}=4.00260 ~\mathrm{u}$ and

$1 \mathrm{u}=931.5 \frac{\mathrm{MeV}}{c^{2}}$

The energy released $(Q)$ during the alpha decay of ${ }_{92}^{238} \mathrm{U}$ is __________ MeV