Lecture 18 - atomic physics

what is the theory of relativity

replacing newtonian mechanics when dealing with particle speeds comparable to the speed of light - Einstein

what is the quantum theory

understanding behaviour of atoms in absorption and emission of radiation

all objects emit radiation whose total intensity is proportional to the … of their kelvin temperature

• fourth power

a body that emits all radiation when hot is called a

blackbody

a blackbody … all radiation that are incident on it and will … none, thus it appears …

• absorb

• reflect

• black

examples of blackbodies

• sun

• hot oven or glowing filament of a light globe may be considered as a blackbody radiator

what is a plot of intensity and wavelength

spectrum of black body radiation

total power of the emitted radiation increases as T increases

Stefan Boltzmann law :

P = omega A e T^4

peak of the spectra shifts towards shorter wavelength as T increases

Wien’s Law Equation

wavelength(MAX) x T = (2.9 × 10^-3)

how does an ear thermometer work

measures the amount of infrared radiation emitted by the ear drum, then it converts the amount of radiation into a temperature reading.

increase from 37-38 degrees c is

(273+38/(273+37) = 1.0032 → 0.32% increase

ear thermometer is given by the fourth power of temperature

((273+38/(273+37))^4 =5,564,554,869.945 1.013 → 1.3% increase in radiated power

Planck’s Quantum Hypothesis (1900)

1. the energy of an atomic oscillator can have only certain discrete values (En), that is, energy of oscillator is quantized

   • E(n) = nhf

     • n = quantum number

     • h = planck constant = 6.63 × 10^-34 J.s

     • f = frequency

2. oscillator emit and absorb energy when making a transition from one quantum state to another in the form of a single quantum energy, energy of radiation is quantised

quantised vs NOT quantised examples

• quantised = energy of a staircase

  • the person can have only certain discrete values of PE when climbing steps

• not quantised = energy of a slide

  • the child can have any value of PE when sliding

observations of the photoelectric effect

• electrons are ejected when light strikes a metal surface

• photocurrent is proportional to light intensity

  • an increase in intensity of the light beam means more photons are incident, so more electrons will be ejected but energy of each photon is not changed

• emission is instantaneous

• max KE of electron is proportional to frequency

• max KE is not proportional to intensity of light

• no electron emission below frequency fc

• max KE can be measured by reversing the terminals of the battery

• max KE = eVs

  • Vs = stopping potential

work function (Wo)

minimum energy required to eject an electron from a material measured in eV

stopping voltage Vs

voltage at which no electron reaches the collector

photons

light ought to be emitted in packets or quanta, since all energy ultimately comes from a radiating source, this suggests that light is transmitted as tiny particles, or photons, in addition to waves

Einstein’s Photon Theory

• quantum theory can explain photoelectric effects

hf = (energy needed to release an e) + (KE of e)

hf = Wo + max KE \

NOTE: one photon ejects one electron only

E = hf = hc/wavelength

• E = energy of photon

• h = Planks constant

• c = speed of light

• f = frequency

E = energy of photon / …

• energy of an electron

number of photons emitted

total energy emitted by light global / energy of one photon

Find the maximum KE and speed of electrons ejected from

a sodium surface, when illuminated by light of λ = 410 nm.

Wo= 2.28 eV.

E = hf = hc/wavelength = (6.63 × 10^-34)(3×10^8)/(410×10^9)(1.6×10^-19)

= 3.02 eV;

hf = Wo + max KE

max KE = hf - Wo

3.03 - 2.28 = 0.75 eV

max KE = ½ mv²

v = sqrt((2 * max KE) / m)

v = sqrt((2 × 0.75(1.6 × 10^-19))/9.1×10^-31)

= 5.1 × 10^5 m/s

will brighter light eject more electrons from a surface than dimmer light of the same frequency?

yes, because brighter light means more intensity - which means more photon/m².s

will high frequency light eject more electrons than low frequency light? assume f > fc and both sources are of the same brightness

no, only the KE of electrons will increase with increasing frequency

when you are at the beach which radiation is more likely to cause sunburn, UV or infrared?

f(uv)>f(ir)

therefore E(uv)>E(ir)

therefore, UV is more likely to cause sunburn

applications of the photoelectric effect

• burglar alarms

• smoke detectors

• automatic door opener

• light meters

• movie sound track reader

gas heated in a discharge tube emits light only at…

• characteristic frequencies, called line spectrum

• line spectrum works as a fingerprint for identification of the gas

when electron makes upward jump (transition it absorbs … When electron makes downward jump it …. energy

• energy

• emits

A photon is emitted as a hydrogen atom undergoes a

transition from the n = 6 state to n = 2 state.

Calculate the:

a. energy

b. wavelength

c. frequency of the emitted photon.

Ionisation Energy

minimum energy required to ionise the atom at ground state

• hydrogen atom is 13.6 eV

• negative sign means that the energy is to be supplied to the electron to make it an upward transition

From the energy level diagram calculate the energy

and wavelength of the photon emitted when an

electron makes a transition from n = 2 to n = 1?