Two radioactive materials A and B have decay constants $$25 \lambda$$ and $$16 \lambda$$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time $$\frac{1}{a \lambda}$$. The value of a is _________.

In the hydrogen spectrum, $$\lambda$$ be the wavelength of first transition line of Lyman series. The wavelength difference will be "a$$\lambda$$'' between the wavelength of $$3^{\text {rd }}$$ transition line of Paschen series and that of $$2^{\text {nd }}$$ transition line of Balmer series where $$\mathrm{a}=$$ ___________.

$${x \over {x + 4}}$$ 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 ______________.