Quantum Physics
Why Quantum Physics?
It is a theory needed to describe physics on a microscopic scale, such as on the scale of atoms, molecules, electrons, protons, etc.
Classical theories:
Newton – Mechanical motion of objects (F = ma) Maxwell – Light treated as a wave
neither of these theories quite work for
Classical world is
Deterministic:
Knowing the position and velocity of
all objects at a particular time
Future can be predicted using known laws of force and Newton's laws of
motion.
Quantum World is
Probabilistic:
Impossible to know position and velocity
with certainty at a given time.
Only probability of future state can be predicted using
known laws of force and equations of quantum
mechanics.
Inadequacies of classical
theory
Region of Atomic Dimension Stability of atoms
Spectrum of Black body radiation
Observed variation of specific heat of metals and gases Discrete spectra of atoms
Observed phenomena: Photoelectric effect, Compton
R r
Ernest Rutherford used alpha rays to discover the nucleus of the atom. The nucleus was positvely charged and contained almost all of the mass of the atom. Most of the atom was empty space.
Electron cloud
Classical physics required
that this atom is unstable
electrons would fall into
the nucleus in 10
-7sec!
Atomic size
Nuclear size
Bohr model explained how atoms emit lightquanta and their stability. He combined thepostulates of Planck and Einstein to build characteristic energy states that atoms should possess. Model gave excellent agreement with experiment on atomic spectra.(1913)
Bohr proposed a revolutionary model:
An atom with discrete (Quantum) states
– an adhoc model
Black body radiation
1900 - Rayleigh
This was a CLASSICAL
prediction, first made in the late 19th century, that an IDEAL BLACK BODY at thermal equilibrium will emit radiation with INFINITE POWER.
Max Planck resolved this issue by postulating that electromagnetic energy did not follow the classical description, but could only
oscillate or be emitted in DISCRETE PACKETS OF ENERGY proportional to the frequency. He called these packets ‘QUANTA’.
h
E
Photoelectric Effect
No electrons were emitted until the frequency of the light exceeded a critical frequency, at which point electrons were emitted from the surface!
(Recall: small large )
Vary wavelength, fixed amplitude
What if we try this ?
electrons emitted ? No Yes, with low KE Yes, with high KE
Electrons are attracted to the (positively charged) nucleus by the
electrical force
In metals, the outermost electrons are not tightly bound, and can be easily “liberated” from the shackles of its atom.
It just takes sufficient energy…
Classically, we increase the energy of an EM wave by increasing the intensity (e.g. brightness)
Energy A2
But this doesn’t work ??
But this doesn’t work ??
Contd..
An alternate view is that light is acting like a particle
The light particle must have sufficient energy to “free” the electron from the atom.
Increasing the Amplitude is simply increasing the number of light particles, but its NOT increasing the energy of each one!
Increasing the Amplitude does diddly-squat!
However, if the energy of these “light particle” is related to their frequency, this would explain why higher frequency light can
knock the electrons out of their atoms, but low frequency light cannot…
An alternate view is that light is acting like a particle
The light particle must have sufficient energy to “free” the electron from the atom.
Increasing the Amplitude is simply increasing the number of light particles, but its NOT increasing the energy of each one!
Increasing the Amplitude does diddly-squat!
However, if the energy of these “light particle” is related to their frequency, this would explain why higher frequency light can
Contd…
In this “quantum-mechanical” picture, the energy of the
light particle (photon) must overcome the binding energy of the electron to the nucleus.
If the energy of the photon exceeds the binding energy, the electron is emitted with a KE = Ephoton – Ebinding.
The energy of the photon is given by E=hwhere the
constant h = 6.6x10-34 [J s] is Planck’s constant.
In this “quantum-mechanical” picture, the energy of the
light particle (photon) must overcome the binding energy of the electron to the nucleus.
If the energy of the photon exceeds the binding energy, the electron is emitted with a KE = Ephoton – Ebinding.
The energy of the photon is given by E=hwhere the
Quantum ?
The word "quantum" is derived From latin to mean BUNDLE.
Photons
Quantum theory describes light as a particle called a photon
According to quantum theory, a photon has an energy given by
E = h = hc/ h = 6.6x10-34 [J s] Planck’s constant,
after the scientist Max Planck.
The energy of the light is proportional to the frequency (inversely proportional to the wavelength) ! The higher the frequency (lower wavelength) the higher the energy of the photon.
The Electromagnetic
Spectrum
Shortest wavelengths(Most energetic photons)
Shortest wavelengths
(Most energetic photons)
Longest wavelengths
(Least energetic photons)
Longest wavelengths
E = h
= hc/
E = h
= hc/
h = 6.6x10-34 [J*sec]
Do Photons carry
Momentum?
For an object with mass, momentum is given by:
p=mv
photon’s have m=0, so how can it be that the momentum is not zero??
Using relation of energy from theory of relativity for a particle of rest mass m0
4 0 2
2c m c p
E
For photon, m0 =0 therefore E=pc
Using energy of photon E=h and equating both expressions
p = h /
E = h
c
/
Photons carry momentum !!!
Photons also carry energy !!!
Both energy & momentum are inversely proportional to the wavelength !!!
The highest energy photons are those which have
small wavelength (that’s why gamma rays are so dangerous)