Let R_{1} be the radius of the second stationary orbit and R_{2} be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio $${{{R_1}} \over {{R_2}}}$$ is :

Given below are two statements

Statement I : The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample.

Statement II : The half of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time t = 0.

In the light of the above statements, choose the most appropriate answer from the options given below :

At any instant, two elements X_{1} and X_{2} have same number of radioactive atoms. If the decay constant of X_{1} and X_{2} are 10 $$\lambda$$ and $$\lambda$$ respectively, then the time when the ratio of their atoms becomes $${1 \over e}$$ respectively will be :

The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is 2.4 $$\times$$ 10^{39}. The ratio of the proportionality constant, $$K = {1 \over {4\pi {\varepsilon _0}}}$$ to the gravitational constant G is nearly (Given that the charge of the proton and electron each = 1.6 $$\times$$ 10^{$$-$$19} C, the mass of the electron = 9.11 $$\times$$ 10^{$$-$$31} kg, the mass of the proton = 1.67 $$\times$$ 10^{$$-$$27} kg) :