Wavelength-stopping potential dependence

[Krushnaraj Pandya]

Homework Statement

Consider a point source emitting light of wavelength 5000 A. Light from this source is falling on a metallic cathode of photoelectric cell. It is also given that energy of a photon of wavelength 10,000 A is 1.23 eV. If the source of 5000 A is replaced by 2500 A wavelength but emitting same no. of photons in unit time, what will happen to the saturation current and stopping potential respectively?

Homework Equations

eV=KE(max)
no. of electrons ejected=no. of photons colliding (energy above work function)

The Attempt at a Solution

since no. of electrons ejected does not change with change in energy of photon, saturation photocurrent remains same.
halving the wavelength doubles the energy of a photon and therefore the electron, since V and energy of electron=0.5mv^2 are directly proportional. Stopping potential should be doubled, but the answer is given as it is more than doubled. Where am I wrong? I suspect doubling wavelength won't double the KE since work function is not zero- but then how do I arrive at the correct relation?
I'd appreciate some help, thank you

 

[mjc123]

Where did you get your "relevant equation"? Isn't it missing something?

 

[Krushnaraj Pandya]

Where did you get your "relevant equation"? Isn't it missing something?

hf=work function+eV

 

[mjc123]

So if you double hf without changing WF, how will eV change?

 

[Krushnaraj Pandya]

So if you double hf without changing WF, how will eV change?

Right, it will more than double

 

[Krushnaraj Pandya]

Thank you very much for your help :D