Initially a gas of diatomic molecules is contained in a cylinder of volume V₁ at a pressure P₁ and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a volume 2V₁ is given by P₂ . The ratio $${{{P_2}} \over {{P_1}}}$$ is ________.

Suppose that intensity of a laser is $${{315} \over \pi }$$ W/m².
The rms electric field, in units of V/m associated with this source is close to the nearest integer is __________.

$$ \in $$₀ = 8.86 × 10^–12 C² Nm^–2; c = 3 × 10⁸ ms^–1)

If the potential energy between two molecules is given by
U = $$ - {A \over {{r^6}}} + {B \over {{r^{12}}}}$$,
then at equilibrium, separation between molecules, and the potential energy are :

An electron, a doubly ionized helium ion (He⁺⁺) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths $$\lambda $$_e, $$\lambda $$_He⁺⁺ and $$\lambda $$_p is :