How do you find threshold frequency? (given wavelength and KE of electrons)

[fizzicsdummy]

If you are told that a silver surface is irradiated with light having a wavelength of 230 nm that causes electrons to be ejected with 77.67 kJ/mol of kinetic energy, how would you find the threshold frequency?



I know that threshold frequency = W / h. W is the work function and h is Planck's constant.



I seriously don't know where to go from there. Obviously, I would be able to get an answer if I could obtain a value for the work function. However, I don't know what equation would allow me to use the given information (the wavelength and kinetic energy) to find the work function value. If anyone could help me with that, that would be great. Thanks!

 

[Redbelly98]

If 1 mole of electrons has 77.67 kJ of kinetic energy, how much kinetic energy does 1 electron have?

Also, what's the energy of a photon of wavelength 230 nm?

 

[baba89]

To find the threshold frequency in this scenario, we can use the equation E = hf - Φ, where E is the energy of the ejected electron, h is Planck's constant, f is the frequency of the light, and Φ is the work function. We can rearrange this equation to solve for the threshold frequency, which is given by f = (E + Φ) / h.

In this case, we are given the energy of the ejected electron (77.67 kJ/mol) and the wavelength of the light (230 nm). We can use the equation c = fλ, where c is the speed of light, to find the frequency of the light. Rearranging this equation gives us f = c / λ. Plugging in the values for c (3.00 x 10^8 m/s) and λ (230 nm = 2.30 x 10^-7 m), we get a frequency of 1.30 x 10^15 Hz.

Now, we can plug in this value for frequency into our equation for the threshold frequency: f = (E + Φ) / h. We know the energy of the ejected electron (77.67 kJ/mol), so we just need to solve for the work function (Φ). Rearranging the equation, we get Φ = hf - E. Plugging in the values for h and f, we get a work function of 4.08 x 10^-19 J.

Therefore, the threshold frequency for this scenario is 1.30 x 10^15 Hz and the work function is 4.08 x 10^-19 J. This means that any light with a frequency lower than 1.30 x 10^15 Hz will not be able to eject electrons from the silver surface, and the minimum amount of energy required to eject an electron is 4.08 x 10^-19 J.