The maximum kinetic energy of the photoelectrons varies

An electron accelerated through a potential difference '$$V_1$$' has a de-Broglie wavelength '$$\lambda$$'. When the potential is changed to '$$V_2$$' its de-Broglie wavelength increases by $$50 \%$$. The value of $$\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right)$$ is

Maximum kinetic energy of photon is '$$E$$' when wavelength of incident radiation is '$$\lambda$$'. If wavelength of incident radiations is reduced to $$\frac{\lambda}{3}$$ then energy of photon becomes four times. Then work function of the metal is

When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are $$\mathrm{v}_1$$ and $$\mathrm{v}_2$$ respectively. The ratio $$\mathrm{v}_1: \mathrm{v}_2$$ is