Photoelectric Effect And Einstein Photoelectric Equation

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{32} Base Sequence = 12735 String Sequence = 12735 - 3 - 32 **

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Photoelectric Effect And Einstein Photoelectric Equation

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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?
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**The strings**:

(a) and (b) S_{7}P_{3}A_{32} (Force - Push).

(c) S_{7}P_{3}A_{31} (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)mv^{2}-------(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)mv^{2} 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 10^{8})/(6500 x 10^{-10}) = 4.62 x 10^{14} Hz Hertz cycles per second).

Energy of one quantum of light with 650 nm wavelength

= hν = (0.66252 x 10^{-33})(4.62 x 10^{14}) = 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 10^{17} photons.

So, 0.327 x 10^{17} 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 10^{17} = 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.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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