LECTURE 23 SPECTROSCOPY AND ATOMIC MODELS

Instructor: Kazumi Tolich Lecture 23

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¨ 29.1 Spectroscopy

¨ 29.2 Atoms ¤ 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 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 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

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

9 29.3 Bohr’s model of atomic quantization

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¨ 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, 29.3-3, & 29.4-1 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

14 29.4 The hydrogen spectrum

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