The X-Y plane be taken as the boundary between two transparent media M₁ and M₂. M₁ in $z\ge 0$  has a refractive index of $\sqrt[]{2}$  and M₂ with Z < 0 has refractive index of $\sqrt[]{3}.$ A ray of light travelling in M₁ along the direction given by the vector $\overrightarrow{P}=4\sqrt[]{3}\widehat{i}-3\sqrt[]{3}\widehat{j}-5\widehat{k},$  is incident on the plane of separation. The value of difference between the angle of incident in M₁ and the angle of refraction in M₂ will be_______ degree.

The distance of closest approach of an alpha particle fired towards gold nucleus with kinetic energy k is r₀. The distance of closest approach when the alpha particle is fired towards same nucleus with kinetic energy 4k will be

Find the mass number of an atom whose radius is half of that of a given atom of mass number 192.

A nuclear fusion reaction is given by   If atomic mass of He is 4.0026 amu and that of O is 15.9994 amu then the Q-value of the reaction will be approximately

A radioactive simple is undergoing a decay. At any time t₁, its activity is A and another time t₂, the activity is $\frac{A}{5}.$ <!-- [if gte mso 9]><xml> </xml><![endif]--> What is the average life time for the sample?

A sample contains 10^-2kg each of two substances A and B with half lives 4s and 8s respectively. The ration of their atomic weights is 1 : 2. The ratio of the amounts of A and B after16s is $\frac{x}{100}$ . The value of x is ______.