When radiation of wavelength $$\lambda $$ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3$$\lambda $$, the stopping potential is $${V \over 4}$$. If the threshold wavelength for the metallic surface is n$$\lambda $$ then value of n will be __________.

A beam of protons with speed 4 × 10⁵ ms^–1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to :
(Mass of the proton = 1.67 $$ \times $$ 10^–27 kg, charge
of the proton = 1.69 $$ \times $$ 10^–19 C)

An engine takes in 5 moles of air at 20^oC and 1 atm, and compresses it adiabatically to 1/10^th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is________.