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Photoelectric Effect And Einstein Photoelectric Equation
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Photoelectric Effect And Einstein Photoelectric Equation

The photoelectric effect explained by the Einstein photoelectric equation established the particle nature of light.

(a) Sodium metal A is illuminated by a light source producing light of wavelength 650 nm. Sodium metal B is illuminated by a light source producing light of wavelength 325 nm (nanometer). Which light source imparted significant kinetic energy to the emitted electrons if the photoelectric threshold of sodium is 650 nm?

(b) A 0.01 Watts beam of light with wavelength 6500 Å (angstrom) which strikes a photoelectric cell is completely used in the production of photoelectrons. Determine the magnitude of the current that flows in the circuit of the photoelectric cell.

(c) What retarding potential would be required to stop the flow of photoelectrons in a photoelectric cell with sodium metal illuminated by light with wavelength of 325 nm, if 3.06 x 10^{-19 J is used to remove the electron from the metal?}

The strings:

(a) and (b) S₇P₃A₃₂ (Force - Push).
(c) S₇P₃A₃₁ (Force - Pull)

The math:
Pj Problem of Interest is of type force (push). Energy is the capacity to do work which is actualize by force. Light energy can do a pull or push work. The push work is more common. Problems (a) and (b) are push work while problem (c) is pull work. Hence the Pj Problem of Interest here is of type force-push.

Photoelectric effect is the emission of electrons out of a metal by action of ultraviolet light or X-ray. The electrons emitted are called photoelectrons. A photoelectric cell is a device that produces current from the electrons emitted during photoelectric effect. The maximum wavelength for the occurrence of the photoelectric effect is called the photoelectric threshold.

The Einstein Photoelectric Equation states that part of the energy of one quantum of light is used to remove the electron from the metal and the remainder is used to impart the electron with kinetic energy:

E = hν = E_i + (1/2)mv²-------(1).
Where E is the energy of one photon; h is Planck's constant (0.66252 x 10^-33 Js); E_i is the energy required to remove the electron from the metal and (1/2)mv² is the kinetic energy imparted to the electron.

(a) The photoelectric threshold of sodium is 650 nm:
So, the amount of light energy of light with wavelength 650 nm will have just enough energy to remove electron from the sodium metal A with no energy left to impart significant kinetic energy to the electron.
The amount of light energy of light with wavelength 325 nm (much less than the photoelectric threshold of sodium) will be sufficient to both remove electron and impart significant kinetic energy to the electron removed from sodium metal B.
So, the light source illuminating sodium metal B imparted significant kinetic energy to the electrons emitted.

(b) Energy of one quantum of light with wavelength 650 Å is:
E = hν
ν = (velocity of light)/(wavelength of light)
= (3 x 10⁸)/(6500 x 10^-10) = 4.62 x 10¹⁴ Hz Hertz cycles per second).
Energy of one quantum of light with 650 nm wavelength
= hν = (0.66252 x 10^-33)(4.62 x 10¹⁴) = 3.06 x 10^-19 J.
So, number of photons in light with power = 0.01 Watts = 0.01 J/sec is:
0.01/(3.06 x 10^-19) = 0.327 x 10¹⁷ photons.
So, 0.327 x 10¹⁷ photons strkes the metal of the photoelectric cell every second.
So, the same number of photoelectrons will be produced
So, number of Coulombs transferred per sec is:
charge of electron in Coulombs x number of electrons
So, 0.1602 x 10^-18 C x 0.327 x 10¹⁷ = 5.24 x 10^-3 C
One ampere is a flow of electricity at the rate of 1 coulomb per second
So, current produced by beam of light = 5.24 x 10^-3 A = 5.24 mA.

(c) Energy of light with wavelength 325 nm = hν = 6.12 x 10^-19 J.
So, energy used to impart kinetic energy to electron is:
6.12 x 10^-19 - 3.06 x 10^-19 = 3.06 x 10^-19.
One electron volt (eV) is defined as the energy acquired by an electron accelerated by a potential difference of 1V.
1 eV = 0.160206 x 10^-18 J.
The retarding voltage (V) is the voltage that slows the electron down to zero speed such that:
charge of electron x retarding voltage = kinetic energy of electron.
So, eV = 3.06 x 10^-19
So, (0.1602 x 10^-18)V = 3.06 x 10^-19
So, V = (3.06 x 10^-19)/ (0.1602 x 10^-18) = 1.91 V.
So, 1.91 V is the retarding potential needed to prevent the flow of photoelectrons in the sodium photoelectric cell illuminated by light of 325 nm wavelength.

Math

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