The Bohr Model and The principal Quantum Number Physics 12 Adv

Bohr Postulates  Once he saw Balmer’s work, Bohr developed his model  Bohr postulated: 1.Electrons exist in circular orbits 2.Electrons exist only in allowed orbits 3.Electrons do not radiate energy within an orbit 4.Electrons can jump between orbits

principal Quantum Number  Bohr’s model requires the use of the principal Quantum Number (n)  It predicts the line spectra of hydrogen through the energy levels of electron orbitals  Unfortunately, Bohr’s model works well for hydrogen but does not completely predict other atoms

Angular Momentum  Is a conserved vector quantity within a system  Similar to momentum, it involves the mass of an object and velocity but additionally, the radius through which it moves  Break down the units of Planck’s Constant (Js) into standard units  What does this tell us?

Quantized Angular Momentum?  The units of Planck’s constant can be broken down into kg, m and m/s which would be the product of mass, distance and velocity  Angular momentum is the cross product of radius and momentum so it is comprised of the same units  Bohr hypothesized that angular momentum may be quantized which led to the following equation:

Two Key Equations  Coulomb’s Law (Electrostatic Force)  Centripetal Force (Circular Motion)

Setting Coulomb’s Law equal to the centripetal force gives:

If we solve Bohr’s quantized angular momentum equation for velocity, we see:

Bohr Radius  The previous equation can be solved for any principal quantum number you choose; check your answer by solving for n = 1, 2  r 1 =5.29x m  r 2 =2.12x m  These values agree well with the known size of an atom ~ m

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