An electron is released from rest near an infinite non-conducting sheet of uniform charge density '$-\sigma$'. The rate of change of de-Broglie wave length associated with the electron varies inversely as n^th power of time. The numerical value of n is _____.

The ratio of the power of a light source $S_1$ to that the light source $S_2$ is $2 . S_1$ is emitting $2 \times 10^{15}$ photons per second at 600 nm . If the wavelength of the source $S_2$ is 300 nm , then the number of photons per second emitted by $S_2$ is __________ $\times 10^{14}$.

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $$10.2 \mathrm{~V}$$. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given hc $$=1245 \mathrm{~eV} \mathrm{~nm}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$$).

An atom absorbs a photon of wavelength $$500 \mathrm{~nm}$$ and emits another photon of wavelength $$600 \mathrm{~nm}$$. The net energy absorbed by the atom in this process is $$n \times 10^{-4} ~\mathrm{eV}$$. The value of n is __________. [Assume the atom to be stationary during the absorption and emission process] (Take $$\mathrm{h}=6.6 \times 10^{-34} ~\mathrm{Js}$$ and $$\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$$ )