From the given data, the amount of energy required to break the nucleus of aluminium $$_{13}^{27}$$Al is __________ x $$\times$$ 10^$$-$$3 J.

Mass of neutron = 1.00866 u

Mass of proton = 1.00726 u

Mass of Aluminium nucleus = 27.18846 u

(Assume 1 u corresponds to x J of energy)

(Round off to the nearest integer)

The nuclear activity of a radioactive element becomes $${\left( {{1 \over 8}} \right)^{th}}$$ of its initial value in 30 years. The half-life of radioactive element is _____________ years.

A radioactive substance decays to $${\left( {{1 \over {16}}} \right)^{th}}$$ of its initial activity in 80 days. The half life of the radioactive substance expressed in days is ____________.

A particle of mass m moves in a circular orbit in a
central potential field U(r) = U₀r⁴. If Bohr's quantization conditions
are applied, radii of possible
orbitals r_n vary with $${n^{{1 \over \alpha }}}$$, where $$\alpha$$ is ____________.