$${x \over {x + 4}}$$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its

(i) third permitted energy level to the second level and

(ii) the highest permitted energy level to the second permitted level.

The value of x will be ____________.

A hydrogen atom in its first excited state absorbs a photon of energy x $$\times$$ 10^{$$-$$2} eV and excited to a higher energy state where the potential energy of electron is $$-$$1.08 eV. The value of x is ______________.

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ____________.

$$\sqrt {{d_1}} $$ and $$\sqrt {{d_2}} $$ are the impact parameters corresponding to scattering angles 60$$^\circ$$ and 90$$^\circ$$ respectively, when an $$\alpha$$ particle is approaching a gold nucleus. For d_{1} = x d_{2}, the value of x will be ____________.