Chapter 7: Wave Nature of Light Flashcards
frequency (v)
cycles per second (s^-1 or Hz)
wavelength
the distance a wave travels in one cycle
amplitude
the depth of a trough or height of a wave crest
speed (c) =
frequency x wavelength
3.00 x 10^8 m/s in a vacuum
the speed of light, a constant
*Visible light is a type of electromagnetic radiation.described by the previous 3 variables (frequency, amplitude and wavelength)
a wave with higher amplitude =
brighter
a wave with lower amplitude =
dimmer
1A =
10^-10 m
s^-1
(inverse second) x/ PER second
E=nhv
E= energy; n= a positive integer; h = Planck’s constant; (v = frequency)
A solid object emits visible light when it is heated to about 1000K.
Blackbody radiation
Color is related to wavelength and frequency, while temperature is related to energy
the color (and intensity) of the light changes as the temperature changes [E=nhv]
- Any object (including atoms) can emit or absorb on certain quantities of energy
- Energy is quantized; it occurs in fixed quantities, rather than being continuous. Each fixed quantum of energy is called a ‘quantum’.
- An atom changes its energy state by emitting or absorbing one or more quanta of energy
(deltaE = nhv, where n can only be a whole #)
Quantum Theory of Energy
E=hv = hc/wavelength
to find the energy of one photon
(1/frequency) = R (1/n1^2 - 1/n2^2) R = 1.096776x10^7 m^-1
the Rydberg equation; R = the Rydberg constant; for the visible series, n1 = 2, n2 = 3, 4, 5…
an atom’s lowest energy state
the Ground State
deltaE = E(final) - E(initial) =
to find the change in E of an atom that emits (Ef-Ei) or absorbs (Ei-Ef) a photon of light
= -2.18x10^-18J x [(1/n(final)^2) - (1/n(initial)^2)]
wavelength = h/(m x u) or = Planck's constant/speed x mass
Calculating the de Broglie wavelength of an electron
to find the wavelenght of a photon =
wavelength = hc/deltaE
= (Planck’s constant x speed)/change in energy of the atom
ultraviolet–> (n=1) - (n=6)
visible–> (n=2) - (n=6)
infrared–> (n=3) - (n=6)
3 spectral lines emitted by the H atom
[E = mc^2]
Matter and energy are alternate forms of the same entity
All matter exibits properties of both particles and waves; electrons have wave-like motion and, therefore, have only certain allowable frequencies and energies
Matter behaves as if it moves in a wave*
the Wave Particle Duality of Energy and Matter
*the de Broglie wavelength for any particle is given by:
[wavelength = h/mU]
(m= mass and U = speed in meters/second)
6.626x10^-34 J (or kg x m^2/s)
Planck’s constant
Classical Theory:
*Matter is particulate and massive
*Energy is continuousand wavelike
led to…
*Since matter is discontinuous and particulate…
perhaps energy is also discontinuous and particulate
*Since energy is wavelike, perhaps…
matter is wavelike
*Since matter has mass, perhaps…
energy has mass
*Since matter is discontinuous and particulate…
perhaps energy is also discontinuous and particulate–
Observation: Blackbody radiation
Planck’s theory: Energy is quantized–only certain values allowed
*Since matter is discontinuous and particulate…
perhaps energy is also discontinuous and particulate–
Observation: Photoelectric effect
Einsteins’s theory:
light has particulate behavior (photons)
*Since matter is discontinuous and particulate…
perhaps energy is also discontinuous and particulate–
Observation: Atomic line spectra
Bohr’s theory:
energy of atoms is quantized; a photon emitted when electron changes orbit
*Since energy is wavelike, perhaps…
matter is wavelike–
Observation: (Davisson/Germer)-
electron beam is diffracted by metal crystal
de Broglie’s theory:
All matter travels in waves; energy of atom is quantized due to wave motion of electrons
*Since matter has mass, perhaps…
energy has mass
Observation: (Compton)
Photon’s wavelength increases (and momentum decreases) after colliding with an electron
Enstein/de Broglie theory:
mass and energy are equivalent; particles have wavelength and photons have momentum
It is not possible to know both the position and the momentum of a moving particle at the same time;
[change in position * mass * change in speed is greater than or equal to (Planck’s constant/4 * pi)]
The more accurately we know the speed, the less accurately we know the position, and vice versa
Heisenberg’s Uncertainty Principle:
[delta x * mass * delta U >/= (h/4pi)]
9.11 x 10^-31 kg
the mass of an electron
The hydrogen atom has only certain energy levels, which Bohr called ‘stationary states’:
Bohr’s atomic model
Each state is associated with a fixed circular orbit of the electron around the nucleus
(Bohr’s atomic model)
the higher the energy level, the farther the orbit is from the nucleus
(Bohr’s atomic model)
when the H electron is in the first orbit, the atom is in its lowest energy state–the ‘ground state’
(Bohr’s atomic model)
*The atom doesn’t radiate energy while in one of its stationary states
(Bohr’s atomic model)
*The atom changes to another stationary state only by emitting or absorbing a photon
(Bohr’s atomic model)
the energy of the photon (hv) equals the difference between the energies of the two energy states
(Bohr’s atomic model)
when the E electron is in any energy state higher than n=1, the atom is in an excited state
(Bohr’s atomic model)
