Here students can locate TS Inter 2nd Year Physics Notes 12th Lesson Dual Nature of Radiation and Matter to prepare for their exam.
TS Inter 2nd Year Physics Notes 12th Lesson Dual Nature of Radiation and Matter
→ Cathode rays: Cathode rays are produced in a discharge tube at a pressure of 0.001 mm and at a potential of 10,000V.
- Cathode rays consists of a steam of fast moving negatively charged particles.
- Speed of cathode rays ranges about 0.1 to 0.2 times light velocity (3 × 108m/s)
- From Millikan’s oil drop experiment charge on electron was found to be 1.602 × 10-19C.
→ Electron emission: A free electron is held inside a metal surface due to attractive forces of ions.
An electron can come out of the metal surface only if it has got sufficient energy to overcome the attractive force.
→ Work function (Φ) : The minimum energy required by an electron to escape from metal surface is called “work function”.
Work function depends on nature of metal.
Note:
In metals, work function of platinum is highest Φp = 5.65 eV,
Work function of caesium is lowest Φp = 2.14.
→ Electron volt (eV): One electron volt is the energy acquired by an electron when it is accelerated through a potential of 1 volt.
1 eV= 1.602 × 1019 joules
→ Thermionic emission: In thermionic emission electrons (metal surfaces) are heated to gain sufficient thermal energy to leave the metal surface.
→ Field emission: In field emission strong electric field is applied on metal so that electrons can be pulled out of the metal.
→ Photo-electric emission: When metal surfaces are illuminated with light waves of suitable energy electrons are emitted from metal surface. This process is called”photo electric emission”.
→ Photo electric effect: The process of libe-rating an electron from the metal surface due to light energy falling on it is called “photo electric effect”.
→ Hallwach’s and Lenard’s observations:
I. Lenard allowed ultraviolet light to fall on metal electrodes placed in an evacuated glass tube. He observed that current is flow¬ing in the circuit. When ultraviolet radiations were stopped immediately current flow was also stopped.
II. Hallwach’s conducted experiments on zinc plates exposed to ultraviolet radiation.
- When a negatively charged zinc plate is exposed to U.V. radiation it lost negative charge.
- When a positively charged zinc plate is exposed to U.V. radiation its positive charge increased.
From above observations he concluded that- Negatively charged particles are emitted from zinc plate under the action of U.V. rays.
- When frequency of incident light is lesser than a certian value called thres¬hold frequency electrons are not liberated from zinc surface.
→ Stopping potential: The minimum negative potential required by collector to stop photo current (or) becomes zero is called “cut off voltage (v0)”
Kmax = ev0 (or) \(\frac{1}{2}\)mVmax = ev0
→ Effect of frequency on stopping potential:
- Stopping potential varies linearly with frequency of incident light.
- Every photo surface has a minimum cut off frequency for which stopping potential V0 = 0
→ Laws of photo electric emission
- Photo electric emission is an instanta¬neous process where time delay is 10-9 seconds or even less
- Every photo surface has a minimum cut of frequency v0 called threshold frequency. Photo emission takes place when frequency of incident radiation υ > υ0
- For frequency υ > υ0 photo current is directly proportional to intensity of incident light.
- When frequency of incident light υ > υ0 kinetic energy of photo electron is directly proportional to frequency υ.
i. e., KE ∝ υ (i.e., υ > υ0)
→ Photo electric effect: Wave theory of light As per wave theory photo electric emission must follow the following rules.
- When intensity of light is high energy absorbed by electrons is also high so liberation of electron and its kinetic energy must depend on intensity of light.
- Threshold frequency limit should not exist.
- Energy absorption by electrons from incident light waves is a slow process. Explicit calculations estimated that it may take hours together to liberate electrons from given metal surface. Practically photo electric effect is not at all obeying any prediction from wave theory of light.
→ Einstein’s photo electric equation: According to Einstein radiation consists of discrete units of energy called quanta of energy radiation.
Energy of quanta called photon in light E = hυ
Maximum kinetic energy of photo electron Kmax is the difference of energy of incident radiation (hυ) and its work function (t)>).
Kmax = hυ – Φ (when υ > υ0)
or \(\frac{1}{2}\)Vmax = h(υ – υ0)
Work function Φ0 = hυ0
→ Millikan’s verification of photo electric equation : Millikan practically verified Einstein’s photo electric equation and found slope of v0 – υ graph is \(\frac{h}{e}\). He calculated h value from \(\frac{h}{e}\) value obtained from υ0 – υ graph. It coincides with h’ value obtained by other scientists.
→ Particle nature of light: In photo electric effect energy of quanta interacted with electrons. Energy of quanta E = hυ, momentum p = \(\frac{\mathrm{hv}}{\mathrm{c}}\)
Since energy quanta has momentum p and a fixed value of energy it is treated as particle. Energy quanta of light is called photon.
→ Properties of photons:
- Energy of photon E = hυ, momentum p = \(\frac{\mathrm{hv}}{\mathrm{c}}\)
- In interaction of radiation with matter light quanta will behave like particles.
- Photons are electrically neutral. So they are not deflected by electric and magnetic fields.
- In photon – particle collision total energy and total mometum are conserved. On collision photon will totally loose its enery and momentum.
Note : In collision between photon and particles total number of photons may not be conserved.
→ Dual nature of light : Light shows wave nature in physical phenomena like interference, diffraction and polarisation.
Light shows particle nature in explaining the phenomena like photo electric effect and compton effect.
So we will consider either wave nature or particle nature depending on the experiment.
Ex:- In case of human eye light gathering by eye lens is explained with wave nature. Where as absorption of energy by rods and cones in retina are explained by particle nature of light.
→ de – Broglie hypothesis: Radiation has dual nature i.e., energy can exist as a wave or as a particle. He assumed that like energy matter will also have dual nature, i.e., matter will have energy and wave nature.
Wave length associated with moving particle λ = \(\frac{h}{p}=\frac{h}{m v}\) = is called de – Broglie wave length.
Experimental results proved wave nature of matter.
→ Heisenberg’s uncertainty principle: According to Heisenberg’s uncertainty principle we cannot exactly find both momentum and position of an electron at the same time.
→ Davisson and Germer experiment: It verified de-Broglie hypothesis.
→ Photo cell: A photo cell will convert light energy into electrical energy. In these cells intensity variation of light is converted into charges in electrical current. They are widely used in recording and reproduction of sound, automatic switches and in automatic counters.
→ Energy of photon E = hυ ⇒ E = \(\frac{\mathrm{hc}}{\lambda}\)
Maximum kinetic energy of photo electron Kmax = eV0
→ Work function Φ0 = hυ0 ‘ υ0 = \(\frac{\phi_0}{\mathrm{~h}}\)
Einsteins’s photo electric equation
Kmax = hυ – Φ0 or eV0 = hυ – Φ0
Where V0 = Stopping potential.
→ de – BrogUe wave length, λ = \(\frac{h}{p}=\frac{h}{m v}\) or \(\frac{h}{p}=\frac{c}{v}\) = λ
→ Kinetic energy of electron in electric field K = eV
Wavelength, λ = \(\frac{h}{p}=\frac{h}{\sqrt{2 m k}}=\frac{h}{\sqrt{2 m e V}}\)