The de-Broglie wavelength of a particle having kinetic energy E is $$\lambda$$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value?

In a photoelectric experiment ultraviolet light of wavelength 280 nm is used with lithium cathode having work function $$\phi$$ = 2.5 eV. If the wavelength of incident light is switched to 400 nm, find out the change in the stopping potential. (h = 6.63 $$\times$$ 10^$$-$$34 Js, c = 3 $$\times$$ 10⁸ ms^$$-$$1)

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000$$\mathop A\limits^o $$. What is the maximum kinetic energy of the emitted photoelectron?

An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :