Half life of a radioactive element is $10\, days$. The time during which quantity remains $1/10$ of initial mass will be .........$days$

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]

A source contains two phosphorous radio nuclides $_{15}^{32} P \left(T_{1 / 2}=14.3 d \right)$ and $_{15}^{33} P \left(T_{1 / 2}=25.3 d \right) .$ Initially, $10 \%$ of the decays come from $_{15}^{33} P$ How long one must wait until $90 \%$ do so?

The initial activity of a certain radioactive isotope was measured as $16000\ counts\  min^{-1}$. Given that the only activity measured was due to this isotope and that its activity after $12\, h$ was $2000\ counts\ min^{-1}$, its half-life, in hours, is nearest to

If $20\, gm$ of a radioactive substance due to radioactive decay reduces to $10 \,gm$ in $4 \,minutes,$ then in what time $80\, gm $ of the same substance will reduce to $10 \,gm$

Half-life of a substance is $10$ years. In what time, it becomes $\frac{1}{4}\,th$ part of the initial amount ........$years$