The rest mass of an electron as well as that of positron is $0.51\, MeV$. When an electron and positron are annihilate, they produce gamma-rays of wavelength(s)

A radioactive sample consists of two distinct species having equal number of atoms $N_0$ initially. The mean-life of one species is $\tau $ and of the other is $5\tau $. The decay products in both cases is stable. The total number of radioactive nuclei at $t = 5\tau $ is

Let $N_{\beta}$ be the number of $\beta $ particles emitted by $1$ gram of $Na^{24}$ radioactive nucler (half life $= 15\, hrs$) in $7.5\, hours$, $N_{\beta}$ is close to (Avogadro number $= 6.023\times10^{23}\,/g.\, mole$)

Draw a graph of the time $t$ versus the number of undecay nucleus in a radioactive sample and write its characteristics. 

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]

Radioactive material $'A'$ has decay constant $8 \lambda$ and material $'B'$ has decay constant $ ' \lambda '$. Initially they have same number of nuclei . After what time, the ratio of number of nuclei of material $'B'$ to that $'A'$ will be $\frac{1}{e}$ ?