A nucleus with mass number 220 initially at rest emits an alpha particle. If the $$Q$$ value of reaction is $$5.5 ~\mathrm{MeV}$$. Calculate the value of kinetic energy of alpha particle

The radius of hydrogen atom in the ground state is 0.53$$\mathop A\limits^o $$. After collision with an electron, it is found to have a radius of 2.12$$\mathop A\limits^o $$, the principal quantum number $$n$$ of the final state of the atom is

In accordance with the Bohr's model, the quantum number that characterises the Earth's revolution around the Sun in an orbit of radius $$1.5 \times 10^{11} \mathrm{~m}$$ with orbital speed $$3 \times 10^4 \mathrm{~ms}^{-1}$$ is [given, mass of Earth $$=6 \times 10^{24} \mathrm{~kg}$$]

If an electron is revolving in its Bohr orbit having Bohr radius of 0.529$$\mathop A\limits^o $$, then the radius of third orbit is