The minimum energy required to produce the photoelectric effect in a particular

Question

The minimum energy required to produce the photoelectric effect in a particular metal is 198 kJ/mol. What wavelength does this correspond to? (Remember that there are 6.022x10^23 photons/mol.) which of the following wavelengths and frequrencies would produce the photoelectric effect? 536 nm, 675 nm, 6*10^12 s^-1, 8*10^17.

I got 604 nm for the wavelength. And I chose 675 nm, 6*10^12 s^-1, 8*10^17 s^-1. But I got it wrong. My thinking was that in order to produce the photoelectric effect, the wavelength and frequency has to be stronger than the given energy. Why am I wrong? What is the correct answer?

Explanation / Answer

WL = h c / E

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

then

E = 198 kJ/mol * 1 mol / 6.022*10^23 * 1000 J / 1 kJ = 3.287*10^-19 J/photon

WL = (6.626*10^-34)(3*10^8 )/(3.287*10^-19)

WL = 6.047*10^-7 m

WL in nm = (6.047*10^-7)(10^9) = 605 nm

Therefore, the wavelenght must be lower than 605 nm

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