1.3 Rutherford, Planck, and Bohr *** Flashcards
Earnest Rutherford
an atom has a dense, positively charged nucleus which accounts for only a small portion of the atom’s volume
Max Planck
- developed the first quantum theory:
- energy emitted as electromagnetic radiation from matter comes in discrete bundles called quanta
- Planck’s relation (equation): determines the energy of a quanta
quanta (quantum is singular)
discrete bundles of energy emitted as electromagnetic radiation from matter
electromagnetic radiation
produced by the vibration of charged particles with electrical and magnetic properties (travels at the speed of light)
Planck’s relation (energy of a quantum)
- E = hf
- E = energy of a quanta
- h = Planck’s constant = 6.626 x 10-34 J ∙ s
- f = frequency of the radiation (f is sometimes designated by the Greek letter, nu: ν )
***of note:
v = fλ
or
c= fλ
c = speed of light (3 x 108m/s)
Niels Bohr
- developed the Bohr model
- angular momentum of an electron
- energy of an electron
- orbit
- ground state and excited state
Bohr model
-
Bohr model: a hydrogen atom consists of a central (+) proton which a (-) electron travels around in discrete, circular orbits
- centripetal forces acting on the electron due to electrostatic force between (+) charged proton and (–) charged electron
angular momentum (of an electron)
- angular momentum: L = nh/2π
L = angular momentum of an electron orbiting the nucleus of a hydrogen atom
n = principal quantum number (any positive integer)
h = Planck’s constant = 6.626 x 10-34 J ∙ s
angular momentum (cont…)
- classical mechanics states an object revolving in a circle (such as an electron), can assume an infinite number of values for its radius and velocity
- using Planck’s quantum theory, Bohr placed restrictions on the possible values of angular momentum
- ***principal quantum number (n) does this
- it is the only variable in the equation (the rest are constants)
- ***principal quantum number (n) does this
- using Planck’s quantum theory, Bohr placed restrictions on the possible values of angular momentum
energy of an electron (eq)
E = - RH / n2
- E = Rydberg unit of energy
- RH = 2.18 x 10-18 J/electron
- n = principal quantum number
- ***E ∝ n (∝ means directly proportional)
- the energy of an electron increases - becomes less negative (closer to zero) - the farther out it is from the nucleus (greater n becomes)
- ***E ∝ n (∝ means directly proportional)
atomic orbital (orbit)
- UTD definition: the region of space where there is a high probability of finding an electron
- the pathway an electron follows around a nucleus
- if one could transfer an amount of energy exactly equal to the difference between one orbit and another, this could result in an electron “jumping” from one orbit to a higher one
ground state (n=1)
- n = 1
- ground state of an atom is the lowest energy
- all electrons are in the lowest possible orbit if an atom is in ground state
excited state (n > 1)
- an excited state of an atom is when at least one electron has moved to a subshell higher than normal energy
***all systems tend toward minimal energy → on the MCAT atoms will generally exist in the ground state unless subjected to extreme heat or irradiation
Bohr model
***we know know Bohr’s model is not UTD
***it only accounts for an atom with only 1 electron, not multiple
***it is not possible to pinpoint the velocity and location in space of an electron at any point in time
***electrons are not restricted to specific pathways; but they tend to localize in space
applications of the Bohr model
atomic emission and atomic absorption
***Bohr Model only applies to one-electron systems (such as H+ or Li2+)
atomic emission spectra
- at room temp, the majority of atoms are in the ground state
- heat or irradiation can excited electrons to higher energy states
- Absorb light
- Higher potential
- Excited state
- Distance (farther from nucleus)
- heat or irradiation can excited electrons to higher energy states
- the lifetime of an excited state is brief → electrons return rapidly to ground state → electrons emit discrete amounts of energy in the form of photons
Figure 1.5 Atomic Emission of a Photon as a result of a ground state transition
atomic emission spectra
- emission spectrum: the spectrum of frequencies of electromagnetic radiation (energy) emitted due to an electron transitioning from a higher energy state to a lower energy state
- the electromagnetic energy emitted is in the form of a photon
- there are many possible electron transitions for each atom of an element
- each transition has specific energy differences
- the energy of the emitted photon is = the energy difference between the two states
- this difference is quantized, not continuous (stairs vs ramp)
- the result is a spectrum of the specific wavelengths/frequencies (fluorescence)
- what we see is the color of the emitted light
- we can use this spectrum to identify elements
- what we see is the color of the emitted light
- the result is a spectrum of the specific wavelengths/frequencies (fluorescence)
- this difference is quantized, not continuous (stairs vs ramp)
- the energy of the emitted photon is = the energy difference between the two states
- each transition has specific energy differences
- there are many possible electron transitions for each atom of an element
- the electromagnetic energy emitted is in the form of a photon
line spectrum (atomic emission spectrum)
Each line on the spectrum corresponds to a specific electron transition
energy of photon (eq): electromagnetic energy of emitted photon from electron energy transition
E = energy of a emitted photon
h = Planck’s constant (6.626 x 10-34 J ∙ s)
c = speed of light (3 x 108 m/s)
λ = wavelength of the radiation
*** E = hf = hc/λ
****energy is inversely proportional to wavelength
-when an electron returns from an excited state to a ground state, it releases a discrete amount of energy in the form of a photon
Bohr model of hydrogen atom:
- Lyman series
- Balmer series
- Paschen series
group of hydrogen emission lines corresponding to transition levels:
- Lyman series: n ≥2 to n =1
- Balmer series: n ≥3 to n =2
- Paschen series: n ≥4 to n =3
the energy associated with a change in the principal quantum number (n) from a higher initial value to to a lower final value
- combined from Planck’s and Bohr’s equations
***unlike other equations → this is initial* minus *final
positive (+) E → emission
negative (-) E → absorption
- the energy of an emitted photon corresponds to the difference in energy between the higher-energy initial state and the lower-energy final state
atomic absorption spectrum
- when an electron transitions from a lower energy level to a higher energy level, it must absorb a specific level of energy in order to do so
- each element absorbs energy at different, specific wavelengths (λ)
- elements in the gas phase are identified using the absorption spectra
- each element absorbs energy at different, specific wavelengths (λ)
atomic emission spectra and atomic absorption spectra
- each element has a characteristic set of energy levels specific to that element
- when an electron moves from a lower energy level to a higher energy level → it must absorb the right amount of energy to do so
- when an electron moves from a higher energy level to a lower energy level → it must emit the right amount of energy to do so
- this energy is in the form of light (photon)
***the amount of energy an electron must absorb or emit is the same when transitioning between the same two levels
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