Physics (Quantum)

Conditions for electromagnetic radiation (photon) to emit electrons from metal

1. Photon Energy equal or greater than the work function of metal

2. Photon Frequency equal or greater than the threshold frequency of metal

Photoelectric effect

Particulate Nature & Failure of Wave Theory

1. The emission of e- from a metal surface when EM radiation of a sufficiently high frequency is incident on it

2. Particulate Nature

• EM radiation consists of packets of energy called photons with energy E=hf

• An e- is only emitted if f of a single incident photon is greater than or equal to metal’s threshold frequency

3. Failure of Wave Theory

• Wave energy is continuous and depends on intensity(amp) not frequency

• Continuous wave energy would build up over time, meaning frequency should eventually cause emission if illuminated long enough

• Contradicts immediate emission of e- as long as frequency of photon is greater than threshold frequency

Energy of a single photon

E = hf = E = (hc)/λ

Momentum of a single photon

λ = h/p

E = pc

Why sound waves dont have particle-like properties

1. λ=h/p

2. λ of sound varies frm 20Hz to 20kHz and speed of sound id 340

3. p is very small

4. force associated with any change in p is extremely hard to detect

Why ordinary objects (even raindrops) dont exhibit wave-like properties

1. λ=h/p

2. as mass of object is much larger than h, λ is extremely small

3. diffraction significant if λ = slit width and its very hard to construct such a small slit width

4. diffraction shows wave-like properties; no diffraction no wave-like properties

visible light λ

400-700nm

UV < red

light

E = hf = hc/λ

c = fλ

rate of emission of photons

p = ne/t

n is no. of photons

e is energy of a photon

Energy levels

E = hc/λ

longest λ = smallest diff in E

total no. of spectral lines

n=no. of energy levels(including base)

n(n-1)/2

Excitation of atom

1. Shoot e- (electron gives fraction of its energy)

• Energy > or = energy level diff

2. Shoot photon (photon absorbed completely)

• Energy = energy level diff

De-excitation of atom

1. Emits photon of wavelength of energy equal to the energy transition

2. As photon energy is discrete, the difference in energy levels, and hence energy levels of atom must be discrete

Heisenberg Position-Momentum Uncertainty

uncertainty xp >= h

Defn: if a measure of the position of a particle is made with uncertainty x and a simultaneous measurement of its momentum in same direction is uncertainty p,

• product of both uncertainties never less than h

uncertainty x = length of container

allowed energy levels

KE = p²/2m

= (h²/wavelength²)(1/2m)

wavelength = 2L/n

En=(h²/8mL²)n²

Line Spectra

How it works - electrons absorb energy equal to energy level difference, and get excited, then de-excites emitting photons in all directions

Emission → series of separate bright lines of definite wavelength or F on dark background

Absorption → continuous spectrum crossed by dark lines due to some missing frequencies

How line spectra show energy lines

1. Energy levels are discrete, transitions occur only between these levels

2. During downward transition, F of photon = (Ei - Ef)/h

3. This means F also discrete, producing a line spectrum

Calculate PD of e- to be accelerated so its wavelength = 0.4nm

KE gain = EPE loss

KE = qV

sub into: wavelength = h/(2mKE)^(1/2)

ionisation energy

ground state energy in J

Why are energy levels -ve?

1. When energy level of atom is 0ev, this is where electron just breaks free from atom

2. When atom is at -ve energy level, its electron is bounded to nucleus by electric attractive force since nucleus and electron are oppositely charged

3. Atom needs to gain energy to cause electron to break free

Electron particle nature

Diffraction is a property unique to waves

• When e-s passes through a thin crystalline graphite target, they form a pattern of concentric fringes on a screen, which is a characteristic of waves interferencd