The kinetic energy of an electron, $$\alpha$$-particle and a proton are given as $$4 \mathrm{~K}, 2 \mathrm{~K}$$ and $$\mathrm{K}$$ respectively. The de-Broglie wavelength associated with electron $$(\lambda \mathrm{e}), \alpha$$-particle $$((\lambda \alpha)$$ and the proton $$(\lambda p)$$ are as follows:

A monochromatic light wave with wavelength $$\lambda_{1}$$ and frequency $$v_{1}$$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $$45^{\circ}$$ and $$30^{\circ}$$ respectively, then the wavelength $$\lambda_{2}$$ and frequency $$v_{2}$$ of the refracted wave are:

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $$\mathrm{W}$$ on earth will weigh on that planet: