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 ___________.

The surface of a metal is illuminated alternately with photons of energies E₁ = 4 eV and E₂ = 2.5 eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is _____.

A beam of electrons of energy E scatters from a target having atomic spacing of 1 $$\mathop A\limits^o $$. The first maximum intensity occurs at $$\theta $$ = 60^o. Then E (in eV) is ______.
(Planck constant h = 6.64 × 10^–34 Js,
1 eV = 1.6 × 10^–19 J, electron
mass m = 9.1 × 10^–31 kg)