Question

Question #52400

Answer 1

The longest wavelength would be `lambda = 2.74 xx 10^(-7) m`

Explanation:

The equation of the photoelectric effect reads

`K = E - psi`

where `psi` is the work function of the metal.

For the maximum wavelength able to eject a photoelectron, we assume there will be no kinetic energy remaining in that electron. Then,

`E = psi`

or, using the Planck relation between energy and wavelength,

`(hc)/lambda = psi`

Changing the subject of this formula, we get

`lambda = (hc)/psi = ((4.14xx10^(-15)"eVs")(3.00xx10^8m/s))/(4.54 eV)`

(You will note I have used a value for `h` that includes eV in its units. If you had used the value that has J in the units, you would divide by `1.6xx10^(-19) (eV)/J` to make the conversion.)

The above calculation gives us the result: `lambda = 2.74 xx 10^(-7) m`

Any wavelength longer than this, and thus lower in frequency will possess too little energy for the task.