If an electron emits 3 eV of energy, what is the corresponding wavelength of the emitted photon?

The wavelength of the emitted photon is 413.6 nm

Explanation:

Given;

energy of the emitted photon, E = 3 eV = 3 x 1.602 x 10⁻¹⁹ J

speed of light, c  = 3 x 10⁸ m/s

The energy of the emitted photon is given by;

E = hf

where;

h is Planck's constant = 6.626 x 10⁻³⁴ J/s

f is the frequency of the light = c / λ

λ is the wavelength

Therefore, the wavelength of the emitted photon is 413.6 nm

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach