The energy of a hydrogen atom in the ground state is $$-$$ 13.6 eV. The energy of a He⁺ ion in the first excited state will be

An alpha nucleus of energy $${1 \over 2}$$ mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

In the nuclear decay given below

$${}_Z^AX \to {}_{Z + 1}^AY \to {}_{Z - 1}^{A - 4}B{}^ * \to {}_{Z - 1}^{A - 4}B,$$

the particles emitted in the sequence are

In a Rutherford scattering experiment when a projectile of charge z₁ and mass M₁ approaches a target nucleus of charge z₂ and mass M₂, the distance of closest approach is r₀. The energy of the projectile is