S10P1CLec28B

S10P1CLec28B - Physics 1C Lecture 28B "Splitting the...

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Physics 1C Lecture 28B "Splitting the atom is like trying to shoot a gnat in the Albert Hall at night and using ten million rounds of ammunition on the off chance of getting it. That should convince you that the atom will always be a sink of energy and never a reservoir of energy." --Ernest Rutherford
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Bohr Atom From last time we found that to ±nd the radius of the orbit of an electron in a hydrogen atom is: We also found that when n = 1, the orbit is called the Bohr radius, (a o = 0.0529nm). So, in general we have: r n = n 2 a o We also found that total energy of the atom to be: r n = n 2 h 2 m e k e e 2 E tot = KE + PE elec = 1 2 m e v 2 k e e 2 r
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Bohr Atom Plus, from centripetal acceleration we found that: Putting this back into energy we get: m e v 2 = k e e 2 r E tot = 1 2 m e v 2 k e e 2 r = 1 2 k e e 2 r Λ Ν Μ Ξ Π Ο k e e 2 r E tot = 1 2 k e e 2 r Λ Ν Μ Ξ Π Ο But we can go back to the result for the radius (r n = n 2 a o ) to get a numerical result.
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Bohr Atom This is energy of any orbit. Please note the negative sign in the equation. When n = 1, the total energy is –13.6eV. This is the lowest energy state and is called the ground state. The ionization energy is the energy needed to completely remove the electron from the atom. The ionization energy for hydrogen is 13.6eV. E tot = 1 2 k e e 2 n 2 a o Λ Ν Μ Ξ Π Ο = 13.6 eV n 2
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So, a general expression for the radius of any orbit in a hydrogen atom is:
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This note was uploaded on 06/03/2010 for the course PHYS PHYS 1C taught by Professor F during the Spring '00 term at UCSD.

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S10P1CLec28B - Physics 1C Lecture 28B "Splitting the...

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