Question

The “electric eyes” used to open doors automatically are based on the photoelectric effect. The metal surface inside the “eye” [an evacuated glass chamber containing the surface (cathode) and a photocurrent collector (anode)] continuously provides current until the light beam that actuates it is interrupted.

a. What is the maximum kinetic energy of photoelectrons produced by a mercury vapor lamp which emits 436 nm violet light causing the actuation of an electric eye of work function 2.1 eV?

b. What is the velocity of the electron?

Answer 1

Kmax = E − ϕ

E = hf = hc/λ

where the first term is the energy of the absorbed photons (E) with frequency (ƒ) or wavelength (λ)

the second term is the work function (ϕ) of the surface with threshold frequency (ƒ0) or threshold wavelength (λ0)

ϕ = hf0 = hc/
	λ0

which is given as 2.1 ev

now calculating,

Kmax = E − ϕ,

E =hc/λ

λ= 236nm
h= 6.626 *10^-19joule
c= 3*10⁸m/s
hence E= 4.55 *10^-19 joule

ϕ =2.1 ev =3.364570786510^-19

K_max =1.19 *10^-19

now max velocity

v² = 2K_max/mass of elctron

=2*1.19*10^-19/9.10938356 × 10^-31

V²= 0.26*10^-12
V= 0.50*10^-6 m/s