PHOTOELECTRIC EFFECT AND X-RAYS

PHOTOELECTRIC EFFECT: EINSTEIN EQUATION  

LEARNING OBJECTIVES: by the end of the lesson, students should be able to:

1. explain photoelectric effects

2. state the factors that photoelectrons depends upon

3. state Einstein's photoelectric equation and use it to solve simple problems. 

4. explain the production of X-rays and state the types, uses and hazard. 


INTRODUCTION 

          Electrons are ejected from a metal surface when electromagnetic radiation of sufficient frequency falls on a metal surface. A metal emits electrons provided that the wavelength of the radiaton is less than a certain value. If the wavelength is too long, the electrons will not be emitted no matter the intensity and duration of the radiation. For example, when ultraviolet radiation of a particular frequency and wavelength falls on zinc, electrons are emitted by the zinc atom. 

          Therefore, Photoelectric effect is the emission of electrons from a metal plate when it is illuminated by light. 

The maximum kinetic energy of the emitted electrons depend only on the frequency or wavelength of the incident light and not the intensity of the light beam. The minimum energy needed to pull out an electron is called the work function, W₀ of the metal. Threshold frequency, f₀ or wavelength, λ₀ is the minimum frequency or wavelength of light that must be exceeded for electron emission to occur. 

          When a photon or quantum of light energy, E or hf, is incident on a metal, part of this energy known as the work function W₀ liberates the electrons from the metal. The remaining energy gives the liberated electron a kinetic energy of ½mv². This process is represented by the Einstein equation. 

Energy of photon = Work function + kinetic energy

                E = W₀ + Ek 

                hf = hf₀ + ½mv²

                hf = hf₀ + eV

                 hf = (hc)/λ₀+ eV           

Where, W₀ = work function

f₀ = threshold frequency

λ₀ = threshold wavelength

Ek = ½mv² = Energy of  Photoelectrons. 

eV = energy of electrons in electron volts. 



THRESHOLD FREQUENCY is the frequency of light falling on a surface that is sufficient to liberate electrons without giving them kinetic energy. 

WORK FUNCTION of a metal is the minimum energy required to liberate electrons from a metal surface. 

APPLICATIONS OF PHOTOCELLS. 

The photoelectric cell is used in 

  1. the reproduction of sound which is recorded on a movie film. 

  2. photography. 

  3. lux meter to determine the intensity of light.

  4. a burglar alarm. 

  5.  traffic light system.


    

                    Photocell

C = emitter

A = collector. 



                                 Graphs of Kmax (eV against frequency (Hz)


STOPPING POTENTIAL: Stopping potential of a photoelectron is the energy required to stop an accelerating electron. It is equal the maximum kinetic energy

Stopping Potential eVs = Ekₘₐₓ. 

Therefore, Vs =  (hf - W₀)/e 

                            = (Ekₘₐₓ)/e

Where Vs = stopping potential in volt (V)

e = electronic charge = 1.6 × 10‐¹⁹ C.  

Ekₘₐₓ = maximum kinetic energy. 

W₀ = work function in joules (J)



                           X-RAYS

          X-ray was discovered accidentally in 1895 by William Roentgen. In principle, the production of X-rays is the inverse of the photo-clectric effect.


PRODUCTION OF X-RAYS

           X-rays are produced by thermionic emission from hot filament. The electrons produced are accelerated through a high voltage and focused onto a tungsten target. This filament lies inside a curved metal cylinder which acts to focus the emitted electrons on to a tungsten target embedded in a copper block (anode). 

          The high acceleration of the electrons arises from the high negative potential of the metal cylinder relative to the anode. The cylinder is also evacuated. 

          The following energy conversions take place during  X-rays production;

  1. The electrical energy is converted into the thermal energy. 

  2. This thermal energy is converted into the mechanical kinetic energy of the accelerated electrons. 

  3. This is in turn converted into the electromagnetic energy of the X- rays and thermal energy.

TYPES OF X-RAYS

  1. SOFT X-RAYS:  They have low penetrating power and longer wavelengths. 

  2. HARD X-RAYS: They have high penetrating power and shorter wavelengths

CHARACTERISTICS OF X-RAYS

  1. They are electromagnetic waves of very high frequency. 

  2. They have short wavelengths.

  3. They have high penetrating power. 

  4. They travel in a straight line. 

  5. They are diffracted by crystals.  

  6. They are not deflected by electric or magnetic fields. 

  7. They cause fluorescence in zinc sulphide.  

  8. They cause photoelectric effect. 

  9. They ionize gases. 


PRACTICAL APPLICATION OF X-RAYS

   X-rays are used;

  1. for examining the body to locate broken bones or bullets in a patient's leg. 

  2. in airports to detect metals and contraband in baggage. 

  3. in industry to detect crack and flaws in metal casting and welded joints. 

  4. to investigate crystals. 

  5. in treatment of tumours, cancer and some skin diseases. 

  6. to detect alterations in artworks. 

  7. in radiography, radio-therapy and in agriculture to kill germs.  


HAZARDS OF X-RAYS

               Expose to X-rays can;

  1. cause skin burns

  2. cause cancer

  3. destroy body cells. 

  4. cause genetic mutation

  5. damage the body tissues and cause 

leukemia


SAFETY PRECAUTIONS

  1. People who work with X-rays should wear lead coats, and have regular health check. 

                              

                            X-ray tube