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 light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular are of radius 30 cm. The value of B is ___________ $$\times$$ 10^$$-$$7 T.

Given hc = 20 $$\times$$ 10^$$-$$26 J-m, mass of electron = 9 $$\times$$ 10^$$-$$31 kg

A certain metallic surface is illuminated by monochromatic radiation of wavelength $$\lambda$$. The stopping potential for photoelectric current for this radiation is 3V₀. If the same surface is illuminated with a radiation of wavelength 2$$\lambda$$, the stopping potential is V₀. The threshold wavelength of this surface for photoelectric effect is ____________ $$\lambda$$.

Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x : y. The value of x is ___________.