A photocell is used to detect a light beam and sound an alarm if the beam is bro

Question

A photocell is used to detect a light beam and sound an alarm if the beam is broken. When the beam is intact, it strikes a metal with a work function W = 0:40 eV. The electrons liberated from the metal form an electric current that can be measured.

a) If the light beam is caused by a simple incandescent light bulb, what temperature should the lament be so that the peak of its emission is energetic enough to liberate elec- trons?

b) What part of the electromagnetic spectrum do the photons at the peak lie in?

c) If a beam of visible light with wavelength = 550 nm strikes the photocell, what is the maximum kinetic energy of the electrons given off? 1

Explanation / Answer

a) at minimum energy the energy of photons equal the workfunction of the metal

W =h*F (=h*c/lambda)    that is lambda = h*c/W =6.626*10^-34*3*10^8/(0.40*1.6*10^-19) =3.106 micro m

The Wien displacement law (of blackbody radiation) is

lambda = b/T    where b=2900 micro m*K

T = b/lambda =(2900/3.106)= 933.68 K =660.53 C

b)

Visible spectrum is between wavelengths 0.390 micro m (violet) and 0.700 micro m (red). Therefore 3.106 micro m is infrared.

c)

Ek = Ephoton - W = hc/lambda -W =6.626*10^-34*3*10^8/550*10^-9 -0.4*1.6*10^-19 =2.974*10^-19 J =1.859 eV

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