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

According to classical physics, $10^{-15}\ m$ is distance of closest approach $(d_c)$ for fusion to occur between two protons. A more accurate and quantum approach says that ${d_c} = \frac{{{\lambda _p}}}{{\sqrt 2 }}$ where $'\lambda _p'$ is de-broglie's wavelength of proton when they were far apart. Using quantum approach, find equation of temperature at centre of star. [Given: $M_p$ is mass of proton, $k$ is boltzman constant]

Two radioactive elements $R$ and $S$ disintegrate as
$R \rightarrow P + \alpha; \lambda_R = 4.5 × 10^{-3} \,\, years^{-1}$
$S \rightarrow P + \beta; \lambda_S = 3 × 10^{-3} \,\, years^{-1}$
Starting with number of atoms of $R$ and $S$ in the ratio of $2 : 1,$ this ratio after the lapse of three half lives of $R$ will be :

A ${\pi ^0}$ at rest decays into $2\gamma $ rays ${\pi ^0} \to \gamma + \gamma $. Then which of the following can happen

Radioactive element decays to form a stable nuclide, then the rate of decay of reactant $\left( {\frac{{dN}}{{dt}}} \right)$ will vary with time $(t) $ as shown in figure

A radioactive nucleus $A$ with a half life $T$, decays into a nucleus $B.$ At $t = 0$, there is no nucleus $B$. At sometime $t$, the ratio of the number of $B$ to that of $A$ is $0.3$. Then, $t$ is given by