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Painting

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?
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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.

Math

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.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

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