Two particles move at right angle to each other. Their de-Broglie wavelengths are $$\lambda _1$$ and $$\lambda _2$$ respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength $$\lambda _2$$ of the final particle, is given by :

In an interference experiment the ratio of amplitudes of coherent waves is $${{{a_1}} \over {{a_2}}} = {1 \over 3}$$ . The ratio of maximum and minimum intensities of fringes will be :

A thermally insulated vessel contains 150g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to : (Latent heat of vaporization of water = 2.10 × 10⁶ J kg^–1 and Latent heat of Fusion of water = 3.36 × 10⁵ J kg^–1)

Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He⁺ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is :