The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $$\lambda$$. To double the kinetic energy, the incident light must have wavelength:

Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

Find the modulation index of an AM wave having $$8 \mathrm{~V}$$ variation where maximum amplitude of the AM wave is $$9 \mathrm{~V}$$.

A travelling microscope has 20 divisions per $$\mathrm{cm}$$ on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?