Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is $$\sqrt {{a \over 7}{{GM} \over R}} $$ then the value of 'a' is ____________.

[Given : The two planets are fixed in their position]

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 $$\mathop A\limits^o $$. If the speed of electron is 2.2 $$\times$$ 16⁶ m/s, then the current associated with the electron will be _____________ $$\times$$ 10^$$-$$2 mA. [Take $$\pi$$ as $${{22} \over 7}$$]

A particle of mass 9.1 $$\times$$ 10^$$-$$31 kg travels in a medium with a speed of 10⁶ m/s and a photon of a radiation of linear momentum 10^$$-$$27 kg m/s travels in vacuum. The wavelength of photon is __________ times the wavelength of the particle.

A prism of refractive index n₁ and another prism of refractive index n₂ are stuck together (as shown in the figure). n₁ and n₂ depend on $$\lambda$$, the wavelength of light, according to the relation

$${n_1} = 1.2 + {{10.8 \times {{10}^{ - 14}}} \over {{\lambda ^2}}}$$ and $${n_2} = 1.45 + {{1.8 \times {{10}^{ - 14}}} \over {{\lambda ^2}}}$$

The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _____________ nm.