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) :

The graph which shows the variation of the de Broglie wavelength ($$\lambda$$) of a particle and its associated momentum (p) is

In the given nuclear reaction, the element X is

$${}_{11}^{22}Na \to X + {e^ + } + v$$