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Lecture 23 Spectroscopy and Atomic Models

LECTURE 23 AND ATOMIC MODELS

Instructor: Kazumi Tolich Lecture 23

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¨ 29.1 Spectroscopy

¨ 29.2 ¤ The first nuclear experiment ¤ Using the nuclear model

¨ 29.3 Bohr’s model of atomic quantization

¨ 29.4 The Bohr ¤ The stationary states of the ¤ Hydrogen atom energy levels ¤ The hydrogen 29.1 Spectroscopy / demo

¨ A spectrum is recorded in a spectrometer.

¨ Self-luminous objects emit a that depends on the .

¨ Individual atoms produce atomic spectrum, a with spectral lines.

¨ Gases also absorb discrete .

¨ Demo: line spectra Quiz 29.1-1

¨ These spectra are from the same element. Which is an , 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 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

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¨ J. J. Thomson, soon after discovering , 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 crystal. ¤ Beta rays are high-speed electrons emitted by uranium. ¤ Alpha rays (now called alpha particles) consist of nuclei, with mass � = 6.64 ×10 kg, emitted at high speed from a sample. 29.2 The first nuclear physics experiment

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¨ 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. 29.2 Using the nuclear model

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¨ 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 and can be easily knocked off, creating a positive . Quiz: 29.3-1

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¨ 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 would not agree with the emission spectra. Quiz: 29.3-1 answer

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¨ 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

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¨ 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 with an energy equal to the difference in the energies of the states: � = � − � = ℎ�. ¤ An atom can be exited by absorbing energy in collision (). 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 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 , in which nearly all the atoms are.

¨ No 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?

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¨ A 5.5 eV electron can excite either the � = 2 or the � = 3 . Quiz: 29.4-1

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¨ De Broglie showed that the allowed orbits of the Bohr model correspond to standing matter 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

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¨ 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

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¨ 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

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¨ 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

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

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¨ 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. 29.4 The hydrogen spectrum

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

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