QUANTUM PHYSICS
Quantum energy
to explain thermal radn, Planck assumed energy can not be divided into smaller amts and are emitted in discrete 'packets' of energy called quanta (1 packet = 1 quantum)
energy depends on freq, f of source
E = hf
[h: Planck's const = 6.63 × 10^-19J (experimentally found)]

some experiments on light show light's -wave nature (interference, diffraction) & -particle nature (photoelectric effect)

Einstein explained particle nature by assuming light (or other em radn) consists of packets of energy called photons (1 proton has 1 quantum of E)

Photoelectric effect

-electron emission from a substance when light is shone on it
electrons emitted reach plate A => galvanometer gives current reading

max KE found by applying stopping voltage,V_s (min V to just stop electrons from reaching plate A => no reading on galvanometer)
eV_s = ½mv_max²


Laws of photoelectric emission
(1) # of photoelectrons emitted per second ∝ intensity of radn
(2) photoelectrons have KE from 0 to max; KE ∝ freq of radn (ie V_S is independent of intensity)

(3) threshold freq, f₀ = min freq for emission of electrons to occur (below f₀ no electron emission despite intensity & time)

wave theory can't explain (2) & (3)
wave theory suggests radn energy spread wavefront
=> since amt of incident energy on electron is v.small > expect time lapse before electrons have enough energy to escape from surface (experimentally: no time lapse)

Einstein's quantum explanation
-each photon give 1 quantum of E (= hf) to electron
-work function = energy, φ for electron to escape surface
-if hf > work function => excess energy increases KE of electron
Einstein's photoelectric eqn: hf - φ = ½mv_max²
electrons emitted photons absorbed
at threshold freq, f₀; E_photon = hf₀ = φ => ½mv_max² = hf - hf₀ = h(f - f₀)
½mv_max² = eV_s = hf - φ => V_s = hf/e - φ/e [φ/e = +ve const, h/e = constant > grad for all graphs are equal]

Wave-particle duality
photon of freq, f has E = hf = hc/λ
Einstein's energy-mass relatn: E = mc² = hc/λ => λ = h/mc [λ: wave-like property, m: particle-like property]
de Broglie suggested particle w/ momentum, p (=mv) has wave-like properties
de Broglie wavelength, λ = h/mc = h/p

Electron diffraction

electron beam shows diffraction pattern > wave-like
diffraction pattern also shown by neutrons, protons, alpha particles
λ associated w/ electron; ~10^-10m (X-ray region)
diffraction shown when using w.small slit sepn (that of interatomic spacing of crystal)
Evidence for electrons as particles
fixed charge- shown by Milikan's oil drop exp
fixed mass- shown by deflectn of cathode rays by B-filed => circular path of certain radius => therefore e/m same for all electrons; since fixed charge => fixed mass

Spectral lines
-a spectrum- mixture of wavelengths
electric discharge through hydrogen at low pressure > gas emits particular wavelengths [spectrum made up of lines (visible colours, UV, IR)]


Bohr's quantum explaination

in atom electrons move around nucleus in certain orbits
diff orbit => diff energy (KE + PE) for each electron
electron raised to higher orbital (when collide w/ electron of another atom) > gain E
electron transition: electron falls to lower orbit > lose energy (as photons)

hf = E₂ - E₁ (certain change in energy due to certain orbits => specific spectral lines => energy quantised)
zero energy when electron at rest outside atom
=> energy at energy levels: -ve (electron 'falls' into atom losing E as em radn)
ground state: electron in lowest energy state available
excited state: electron raised to higher level => empty level below

Evidence of energy levels- optical line spectra
-line in optical spectra indicates presence of particular freq (=> λ) of light
-lines arise from E_loss through transition(s)
-freq n the quantum of E given by; hf = E₂ - E₁
Emission line spectra

-consists of quite separated bright lines of definite wavelength on dark (black) background
-given by luminous gases & vapours at low pressure (diff element > diff spectrum)
-spectra shows evidence of energy levels in atoms (since atoms only emit & hence accept 'packets' of E of certain values > E quantised)
Absorption line spectra

-occurs when white light passes through coloured gas / vapour
-dark lines occur against continuous spectrum of white light exactly at some wavelength present in line emission spectrum of gas
-atoms of cooler gas absorb light of wavelengths which they can emit => re-radiate wavelength almost immediately but in all dirns => parts of spectrum of wavelengths appear dark compared w/ other wavelengths not absorbed


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