5. An electromagnetic wave of unknown wavelength propagates in the +y direction

Question

5. An electromagnetic wave of unknown wavelength propagates in the +y direction onto a sample of sodium to create a photocurrent. The electromagnetic wave has a B field with a maximum value of 0.47 mT and is polarized in the +z direction. The sample of sodium has a work function of 2.36 eV, and a 0.16 V stopping potential was measured a) Determine the wavelength of light. Could humans see this wavelength of light? b) Write down the wave equation of the electric field component for this EM wave. That is: E -Amplitude cos(phase) [direction

Explanation / Answer

Using Einestein photoelectric effect equation

Energy of photon = Work finction (Wo) + (Vo*e)

Vo is the stopping potential

e is the charge of the electron = 1.6*10^-19 C

then

E = (2.36*1.6*10^-19)+(0.16*1.6*10^-19) = 4.032*10^-19 J

But E = h*c/lamda = 4.032*10^-19

(6.625*10^-34*3*10^8)/lamda = 4.032*10^-19

lamda = 493 nm

since this wavelength is in visible region,hence human can see this wavelength of light

b) E = Emax*cos(wt)

E = (c*Bmax)*cos(w*t)

E = 3*10^8*0.47*10^-3*cos(w*t)

E = 1.41*10^5*cos(w*t) along y-direction

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