A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $${\lambda _A}$$ to $${\lambda _B}$$ after the collision is:

A photoelectric surface is illuminated successively by monochromatic light of wavelengths $$\lambda $$ and $${\lambda \over 2}.$$ If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface is :

When photons of wavelength $${\lambda _1}$$ are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength $${\lambda _2}$$ are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength $${\lambda _3}$$ is used then find the stopping potential for this case :

Radiation of wavelength $$\lambda ,$$ is incident on a photocell. The fastest emitted electron has speed $$v.$$ If the wavelength is changed to $${{3\lambda } \over 4},$$ the speed of the fastest emitted electron will be: