Consider 3^rd orbit of He⁺ (Helium), using non-relativistic approach, the speed of electron in this orbit will be [given K = 9 $$ \times $$ 10⁹ constant, Z = 2 and h (Planck's Constant) = 6.6 $$ \times $$ 10^$$-$$34 J s]

A radioactive X with a half life 1.4 $$ \times $$ 10⁹ years decays to Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1 : 7. The age of the rock is

Hydrogen atom in ground state is excited by a monochromatic radiation of $$\lambda $$ = 975 $$\mathop A\limits^ \circ $$. Number of spectral lines in the resulting spectrum emitted will be

The binding energy per nucleon of and nuclei are 5.60 MeV and 7.06 MeV respectively. In the nuclear reaction

$${}_3^7Li + {}_1^1H \to {}_2^4He + _2^4He + Q$$

the value of energy Q released is