The radius of inner most orbit of hydrogen atom is $$5.3 \times 10^{-11} \mathrm{~m}$$. What is the radius of third allowed orbit of hydrogen atom?

Let R₁ be the radius of the second stationary orbit and R₂ 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 X₁ and X₂ have same number of radioactive atoms. If the decay constant of X₁ and X₂ are 10 $$\lambda$$ and $$\lambda$$ respectively, then the time when the ratio of their atoms becomes $${1 \over e}$$ respectively will be :