LECTURE 23 SPECTROSCOPY and ATOMIC MODELS 29.1 Spectroscopy the Colorful Light from “Neon Signs” 29.2 Atoms Are Due to Atomic Transitions of Various Gas

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LECTURE 23 SPECTROSCOPY AND ATOMIC MODELS 29.1 Spectroscopy The colorful light from “neon signs” 29.2 Atoms are due to atomic transitions of various gas. The first nuclear physics experiment Using the nuclear model 29.3 Bohr’s model of atomic quantization 29.4 The Bohr hydrogen atom The stationary states of the hydrogen atom Hydrogen atom energy levels The hydrogen spectrum 29.1 Spectroscopy / demo

! A spectrum is recorded in a spectrometer.

! Self-luminous objects emit a continuous spectrum that depends on the temperature.

! Individual atoms produce atomic spectrum, a discrete spectrum with spectral lines.

! Gases also absorb discrete wavelengths.

! Demo: line spectra Quiz 29.1-1

! These spectra are from the same element. Which is an emission spectrum, which an absorption spectrum? A. Top is emission; bottom absorption. B. Top is absorption; bottom emission. C. Can’t tell without knowing the element. Quiz 29.1-1 answer

! Top is emission; bottom absorption.

! Every wavelength that is absorbed by the gas is also emitted, but not every emitted wavelength is absorbed. Spectroscopy

! Balmer formula represents the wavelengths of the spectral lines of hydrogen.

91.1 nm ! = 1 1 − () +)

! where ( = 1, 2, 3, … and + can be any integer and + > (. 29.2 Atoms - the raisin-cake model of the atom

! J. J. Thomson, soon after discovering electrons, proposed the raisin-cake model of the atom (“plum-pudding model” actually). ! It was known that electrons are much smaller and less massive than atoms.

! The first observations that atoms have an inner structure came from beta rays and alpha rays emitted from uranium crystal. ! Beta rays are high-speed electrons emitted by uranium. ! Alpha rays (now called alpha particles) consist of helium nuclei, with mass ! = 6.64 ×10)*+ kg, emitted at high speed from a sample. 29.2 The first nuclear physics experiment

! The discovery of large-angle scattering of alpha particles led to the nuclear model of the atom in which negative electrons orbit a small, massive, positive nucleus.

! For fun: Rutherford said “It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.” 29.2 Using the nuclear model

! In the nuclear model, an atom has a nucleus with positively charged protons and neutral neutrons, and negatively charged electrons are orbiting around it.

! Protons and neutrons are both much more massive than electrons.

! Orbiting electrons are very light and can be easily knocked off, creating a positive ion. Quiz: 29.3-1

! Is there something wrong with the nuclear model (like a miniature solar system) of the atom? If so, what is wrong? Choose all that apply. A. No. Everything is fine with the model. B. Yes. Nothing is providing orbiting electrons the centripetal force. C. Yes. Orbiting electrons would collapse into the nucleus in a very short time. D. Yes. The frequency of radiation emitted by an orbiting electron would not agree with the emission spectra. Quiz: 29.3-1 answer

! Yes. Orbiting electrons would collapse into the nucleus in a very short time.

! Yes. The frequency of radiation emitted by an orbiting electron would not agree with the emission spectra.

! The coulomb force by the nucleus is providing orbiting electrons the centripetal force.

! The frequency of radiation emitted by a continuously radiating electron would have a continuous spectrum, rather than the individual frequencies that are actually observed. 29.3 Bohr’s model of atomic quantization

! Bohr model of the atom: ! An electron in an atom can exist only in a stationary state. ! Each stationary state has a discrete well- defined energy. ! An atom can undergo a transition by emitting or absorbing a photon with an energy equal to the difference in the energies of the states: !"#$%$& = !( − !* = ℎ,. ! An atom can be exited by absorbing energy in collision (collisional excitation). Quiz: 29.3-2

! An atom has the energy levels shown. A photon with a wavelength of 620 nm has an energy of 2.0 eV. Do you expect to see a spectral line with wavelength of 620 nm in this atom’s absorption spectrum? A. Yes B. No C. There’s not enough information to tell. Quiz: 29.3-2 answer

! No

! Absorption occurs from the ground state, in which nearly all the atoms are.

! No quantum jump from the ground state has ∆"#$%& = 2.0 eV. ! Every wavelength that is emitted by gas is not absorbed.

Emission transitions Absorption transitions Quiz: 29.3-3

! An atom has the energy levels shown. A beam of electrons with 5.5 eV kinetic energy collides with a gas of these atoms in the ground state. How many spectral lines will be seen? Quiz: 29.3-3 answer

! An atom has the energy levels shown. A beam of electrons with 5.5 eV kinetic energy collides with a gas of these atoms in the ground state. How many spectral lines will be seen?

! 3

! A 5.5 eV electron can excite either the ! = 2 or the ! = 3 energy level. Quiz: 29.4-1

! De Broglie showed that the allowed orbits of the Bohr model correspond to standing matter wave of the electrons. What is the relationship between the wavelengths of the electrons in an atom and the circumferences of the allowed orbits? A. The circumference must be an integer multiple of !. " B. The circumference must be an odd integer multiple of . # C. There is not relationship between the circumference and !. Quiz: 29.4-1 answer

! The circumference must be an integer multiple of !.

! The circumference of an allowed orbit is 2#$ = &!, & = 1, 2, 3, ⋯. 29.4 The stationary states of the hydrogen atom

! The allowed radii of the electron’s orbit in a hydrogen atom is

% !" = $ &'

! $ = 1, 2, 3, ⋯

! &' = 0.0529 nm is the Bohr radius. ! The possible orbits are quantized. 29.4 Hydrogen atom energy levels

! There is an energy level in a hydrogen atom corresponding to each allowed state radius.

! 13.6 eV ! = − % = − " &' &'

! & = 1, 2, 3, ⋯ Quiz: 29.4-2

! How much energy in eV does it take to ionize a hydrogen atom in its ground state? Quiz: 29.4-2 answer

! 13.6 eV

! When a hydrogen atom in the ground state absorbs 13.6 eV of energy, the electron makes a transition to ! = ∞ state (ionization limit), which means that the electron is no longer associated to the nucleus. '(.* +, '(.* +, ! $ − $ = − − = 13.6 eV % ' %- '- 29.4 The hydrogen spectrum

! The Bohr hydrogen atom with discrete energy levels correctly predicts the discrete spectrum of the hydrogen atom.