A piece of bone of an animal from a ruin is found to have $^{14}C$ activity of $12$ disintegrations per minute per gm of its carbon content. The $^{14}C$ activity of a living animal is $16$ disintegrations per minute per gm. How long ago nearly did the animal die? …………$years$ (Given halflife of $^{14}C$ is $t_{1/2} = 5760\,years$ )

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]

The sun radiates energy in all directions. The average radiations received on the earth surface from the sun is $1.4\;kilowatt/{m^2}$.The average earth- sun distance is $1.5 \times {10^{11}}metres$. The mass lost by the sun per day is($1$ day $= 86400$ seconds)

The half-life of a radioactive substance is $48$ hours. How much time will it take to disintegrate to its $\frac{1}{{16}} \,th$ part …………$hour$

The decay constant of a radio isotope is $\lambda$. If  $A_1$ and $A_2$ are its activities at times $t_1$ and $t_2$  respectively, the number of nuclei which have decayed during the time $(t_1 – t_2)$