1.3 Rutherford, Planck, and Bohr ***

Question 1

Earnest Rutherford

Answer 1

an atom has a dense, positively charged nucleus which accounts for only a small portion of the atom’s volume

Question 2

Max Planck

Answer 2

• 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

Question 3

quanta (quantum is singular)

Answer 3

discrete bundles of energy emitted as electromagnetic radiation from matter

Question 4

electromagnetic radiation

Answer 4

produced by the vibration of charged particles with electrical and magnetic properties (travels at the speed of light)

Question 5

Planck’s relation (energy of a quantum)

Answer 5

• 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)

Question 6

Niels Bohr

Answer 6

• developed the Bohr model
  
  • angular momentum of an electron
  • energy of an electron
  • orbit
  • ground state and excited state

Question 7

Bohr model

Answer 7

• 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

Question 8

angular momentum (of an electron)

Answer 8

• 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

Question 9

angular momentum (cont…)

Answer 9

• 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)

Question 10

energy of an electron (eq)

Answer 10

E = - R_H / n²

• E = Rydberg unit of energy
• • R_H = 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)

Question 11

atomic orbital (orbit)

Answer 11

• 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

Question 12

ground state (n=1)

Answer 12

• 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

Question 13

excited state (n > 1)

Answer 13

• 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

Question 14

Bohr model

Answer 14

***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

Question 15

applications of the Bohr model

Answer 15

atomic emission and atomic absorption

***Bohr Model only applies to one-electron systems (such as H⁺ or Li²⁺)

Question 16

atomic emission spectra

Answer 16

• 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)
• 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

Question 17

Figure 1.5 Atomic Emission of a Photon as a result of a ground state transition

Answer 17

Question 18

atomic emission spectra

Answer 18

• 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

Question 19

line spectrum (atomic emission spectrum)

Answer 19

Each line on the spectrum corresponds to a specific electron transition

Question 20

energy of photon (eq): electromagnetic energy of emitted photon from electron energy transition

Answer 20

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

Question 21

Bohr model of hydrogen atom:

• Lyman series
• Balmer series
• Paschen series

Answer 21

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

Question 22

the energy associated with a change in the principal quantum number (n) from a higher initial value to to a lower final value

Answer 22

• combined from Planck’s and Bohr’s equations

***unlike other equations → this is initial* minus *final

positive (+) E → emission

negative (-) E → absorption

Question 23

Answer 23

• the energy of an emitted photon corresponds to the difference in energy between the higher-energy initial state and the lower-energy final state

Question 24

atomic absorption spectrum

Answer 24

• 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

Question 25

atomic emission spectra and atomic absorption spectra

Answer 25

• 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

Question 26

1.3 Concept Check (#1)

Answer 26

Question 27

1.3 Concept Check (#2)

Answer 27

Question 28

1.3 Concept Check (#3)

Answer 28