Orion Nebula: the red light is (mostly) hydrogen Balmer series
Units:
In what follows, we are in the realm of very small:
Size of atoms ∼ 0.1 nm = 10-10m
Size of nucleus ∼ 5 fm = 5x10-15m
Times ∼ 1 ps = 10-12s
Energies ∼ 1 electron Volt (eV) ∼ 1.6x10-19J
In what follows, we'll be using electron-Volts (eV) to measure energy: better for atomic sized objects
Planck's Radiation Law
Black body spectrum:
Consider box of Z different atoms: velocities of each will be random,
but will "average out" to give smooth curve. Energy is equally divided
between different molecules
E = 1/2 m v²
on the average: also average energy increases with temperature.
But suppose light is a particle...
Planck (1900) suggested that E.M. radiation is emitted in lumps (quanta) which became
known as "photons"
f λ = c
(frequency x wavelength = speed)
E = h f
(energy of photon = Planck's constant x frequency)
Energy contained in quantum increases with frequency so costs more
energy to emit short wavelength light.
Planck's constant
h = 6.6 x 10-34 Js = 4.1 x 10-15 eV s
Photons are also particles with a difference: they always travel at c
and can easily be created and destroyed.
Hence at room temperature average
photon has
E ~1/40 eV
E = hf = hc/λ
λ ~ 50000 nm which is very long wavelength I.R.
As temperature increases,
total energy increases
wavelength for maximum decreases
The photo-electric effect also involves light:maybe that can have a
photon explanation.
Einstein and the Photo-electric Effect
Since particles have energy, photons must carry energy (obviously light
has energy: that's how you get a sun tan!)
Einstein (1903): (note this was what he actually got the
Nobel prize for) adapted Planck's hypothesis to say that light is
absorbed in quanta (photons) most energetic electrons in metal need
extra boost to escape:
K.E. = 1/2mv²= hf-φ
where φ is work function: differs for different metals.
Slope is universal ⇒ Planck's constant
So we have to take photons seriously!
The first of many paradoxes:
Electrons are ejected as soon as light strikes (no need for energy
to accumulate), since photons arrive randomly
"Classical" corks bob up and down
"Quantum" corks are either stationary or ejected.
fλ = c
(frequency x wavelength = speed)
E = h f
e.g. orange light λ= 600 nm,
frequency of orange light 4x1014
Energy of photon 2eV
A 60W bulb produces 2x1019 photons each second
Why are we not aware of discrete arrival of photons?
What is light?
Particle? Newton, Descartes
Wave? Young, Huyghens
Yes? Einstein
Light travels as wave, but arrives and departs as particle
The Bohr atom
(Bohr 1917)
Model for H. atom must explain
Spectrum : This implies only photons of certain definite energies are emitted . . .
Rutherford's observation of massive nucleus
Stability
Bohr was able to construct model of electron in orbit round nucleus lets us explain spectrum
of H and ionized He+ but not other atoms
