What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from $$1 \mathrm{~nm}$$ to $$0.5 \mathrm{~nm}$$ ?

Photoelectrons are emitted when photons of energy $$4.2 ~\mathrm{eV}$$ are incident on a photosensitive metallic sphere of radius $$10 \mathrm{~cm}$$ and work function $$2.4 ~\mathrm{eV}$$. The number of photoelectrons emitted before the emission is stopped is

$$\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9\right.$$ SI unit; $$\left.\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right]$$

When light of wavelength '$$\lambda$$' is incident on a photosensitive surface, photons of power 'P' are emitted. The number of photon 'n' emitted in time 't' is [h = Planck's constant, c = velocity of light in vacuum]

When a photosensitive surface is irradiated by light of wavelengths '$$\lambda_1$$' and '$$\lambda_2$$', kinetic energies of emitted photoelectrons are 'E$$_1$$' and 'E$$_2$$' respectively. The work function of photosensitive surface is