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 :
The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is 2.4 $$\times$$ 1039. 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
$${}_{11}^{22}Na \to X + {e^ + } + v$$