Electrons in Atoms

1. Electrons in Atoms 5.3 Physics and the Quantum Mechanical Model

2. Chemistry • Today we are learning to:-1. Understand the relationship between the wavelength and frequency of light2. Understand the reasons for emission spectra • 3. Explain how frequencies of emitted light are related to changes in electron energy • 4. Distinguish between quantum mechanics and classical mechanics

3. Light • How are the wavelength and frequency of light related? • The amplitude of a wave is the wave’s height from zero to the crest. • The wavelength, represented by  (the Greek letter lambda), is the distance between the crests.

4. Light • How are the wavelength and frequency of light related? • The frequency, represented by  (the Greek letter nu), is the number of wave cycles to pass a given point per unit of time. • The SI unit of cycles per second is called a hertz (Hz).

5. Light • How are the wavelength and frequency of light related? • The product of the frequency and wavelength always equals a constant (c), the speed of light.

6. Light • How are the wavelength and frequency of light related? • The wavelength and frequency of light are inversely proportional to each other.

7. 5.1

8. 5.1

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10. 5.1

11. What is the frequency of radiation with a wavelength of 5.00 x 10-8 m? • What is the wavelength of radiation with a frequency of of 5.00 x 1015 Hz? Knowns c = 2.998 x 108 m/s λ = 5.00 x 10-8 m c = λν therefore ν = c/λ ν =2.998 x 108 m/s = 6.00 x 1017 s-1 5.00 x 10-8 m Knowns c = 2.998 x 108 m/s ν = 5.00 x 1015s-1 c = λν therefore λ = c/ν λ =2.998 x 108 m/s = 6.00 x 10-6 m 5.00 x 1015 m

12. for Sample Problem 5.1 • An inexpensive laser that is available to the public emits light that has a wavelength of 650nm. What is the frequency of the radiation. Remember  1nm = 1 x 10-9m (check on page 74 of text book for SI units) Knowns c = 2.998 x 108 m/s λ = 650nm = 6.50 x 10-7 m c = λν therefore ν = c/λ ν =2.998 x 108 m/s = 4.61 x 1014 s-1 6.50 x 10-7 m

13. 5.3 Atomic Spectra • Atomic Spectra • When light from a helium lamp passes through a prism, discrete lines are produced • The frequencies of light emitted by an element separate into discrete lines to give the atomic emission spectrumof the element.

14. 5.3 Atomic Spectra • In the Bohr model: • When the electron has its lowest possible energy, the atom is in its ground state. • Excitation of the electron by absorbing energy raises the atom from the ground state to an excited state. • A quantum of energy in the form of light is emitted when the electron drops back to a lower energy level. • Atomic Spectra

15. 5.3 An Explanation of Atomic Spectra Atomic Spectra • The three groups of lines in the hydrogen spectrum correspond to the transition of electrons from higher energy levels to lower energy levels.

16. 5.3 Atomic Spectra • Main points: • (1905 Special Relativity Theory) Einstein showed that light could be described by packets of energy (quanta) called photons. • (1924) DeBrogliedeveloped an equation that predicts that all moving particles have wavelike behavior (Ex. electrons). This is called ‘the wave particle duality of matter’. (λ = h/p = h/mv) • The wavelike properties of electrons are used in electron microscopes They have much smaller wavelengths than visible light, and can give greater magnification. • Quantum Mechanics

17. 5.3 Atomic Spectra • Main points: • Classical mechanics describes the motions of bodies much larger than atoms, while quantum mechanics describes the motions of subatomic particles and atoms as waves. • The Heisenberg uncertainty principlestates that it is impossible to know exactly both the velocity and the position of a particle at the same time. • Quantum Mechanics

18. The Heisenberg Uncertainty Principle

19. 5.3 Section Quiz. 1. Calculate the frequency of a radar wave with a wavelength of 125 mm. • 2.40 109 Hz • 2.40 1024 Hz • 2.40 106 Hz • 2.40 102 Hz

20. 5.3 Section Quiz. 2. The lines in the emission spectrum for an element are caused by • the movement of electrons from lower to higher energy levels. • the movement of electrons from higher to lower energy levels. • the electron configuration in the ground state. • the electron configuration of an atom.

21. 5.3 Section Quiz. 3. Spectral lines in a series become closer together as n increases because the • energy levels have similar values. • energy levels become farther apart. • atom is approaching ground state. • electrons are being emitted at a slower rate.

22. 2.3 Vocabulary 5.1 Vocabulary • Energy levels:possible electron orbits in Bohr’s model of the atom • Quantum:small whole number unit of energy • Quantum mechanical model: quantum description of the movement of electrons in atoms obtained from solving Schrodinger’s equations • Atomic orbital: region of space where there is a high probability of finding an electron 5.2 Vocabulary • Electron configuration:knocks electrons of atoms to produce ions • Aufbau principle: Electrons occupy orbitals of lowest energy first. • Pauli exclusion principle: Atomic orbitals can hold up to 2 electrons of opposite spin. • Hunds rule: All orbitals of the same energy must have an electron in them before they can pair up. 5.4 Vocabulary • Amplitude:waves height from the origin. • Wavelength:distance between crests. • Frequency: number of waves passing a given point per second. • Hertz: S.I. Unit of frequency 1 Hz = 1s-1 = 1 1/s= 1 cycle per second. • Electromagnetic radiation: Radiation over a broad band of wavelengths. • Spectrum: The result of light being split into its component colors. • Atomic emission spectrum: Spectrum from the light emitted by an element. • Ground state: Lowest energy state of an electron in an atom. • Photons: Quanta of light particles • Heizenberg uncertainty principle: You can’t find the position and velocity of a particle simultaneously

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