Lesson_5.1b_Printable_PPT

Lesson_5.1b_Printable_PPT - Bohr Model of the Atom Bohr was...

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Bohr was familiar with the emission spectrum of hydrogen. When light produced by a hydrogen source is passed through a glass prism, it splits into discrete colors. Bohr Model of the Atom Each color in the spectrum corresponds to a particular energy of radiation. Since these radiations come from atoms of hydrogen, Bohr argued that an atom can only emit radiations of certain frequency. He connected this to the model of the atom because an electron in an orbit is in a particular state of energy.
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Bohr came up with 4 postulates. 1. Electrons assume only certain orbits around the nucleus. These orbits are stable and are called “ allowed " orbits. 2. Each orbit has an energy associated with it. For example the orbit closest to the nucleus has an energy E1 , the next closest E2 and so on. 3. Light is emitted when an electron jumps from a higher orbit to a lower orbit and absorbed when it jumps from a lower to higher orbit. 4. The energy and frequency of light emitted or absorbed is given by the difference between the two orbit energies.
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Bohr argued that the angular momentum of the electron in an orbit is quantized and can have only values that are multiples of h/2 π . For an electron in orbit, the centripetal force to keep it in orbit is provided by the electrostatic force between the electron and the proton iven by the coulomb’s law. given by the coulomb’s law. 2 2 2 mv e k r r = The angular momentum of the electron in orbit is mvr, and when this is quantized, we have: (n = 1, 2, 3. ..) 2 h mvr n π = This gives v = nh/(2 π mr). 2 2 2 ( / 2 ) e m nh mr k r r = 2 2 2 3 4 n h mr =
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If r n is the radius of the n th energy level orbit 2 2 2 2 2 3 4 ke n h r mr π = 2 2 2 2 4 n h r n ke m = The energy E n of an electron is 2 0.0529 nm (for n = 1, 2, 3, 4,. ...) n = 2 2 n n ke E r = - 2 2 4 2 2 2 1 k e m h n = - 2 2 2 2 2 4 2 ke ke m h n = - 2 13.62 eV (for n = 1, 2, 3, 4,. ...) n E n - =
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Example 1 Find the orbital radius and the energy of an electron in the first excited state (n = 2) of a hydrogen atom. What is the speed of the electron in this state? 2 2 2 2 2 2 4 h r ke m π = 0.0529 4 n 0.21 m 2 nm = × = 3.62 2 2 13.62 2 E - = 3.41 eV = - 2 nh v mr = 34 31 9 2 6.63 10 2 9.11 10 0.212 10 - - - × × = × × × × 6 -1 = 1.1 10 m.s ×
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The allowed orbits are characterized by the energy of the electron in that orbit and are labeled n = 1, n = 2, n = 3 and so on. n = 1 n = 2 n = 3 n = 1 corresponds to the lowest energy level E 1 and is called the ground state of the electron. If an electron receives a specific amount of extra nergy from an external source such as heating energy from an external source such as heating or bombardment, it can jump to a higher energy level corresponding to n = 2, 3 and so on corresponding to energies E 2 , E 3 and so on. The electron is then said to be
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This note was uploaded on 05/01/2011 for the course PHY 2049 taught by Professor George during the Spring '11 term at Edison State College.

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Lesson_5.1b_Printable_PPT - Bohr Model of the Atom Bohr was...

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