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 orbits2. Electrons exist only in allowed orbits3. Electrons do not radiate energy within

an orbit4. 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:

nnh

mvr 2

Two Key Equations

Coulomb’s Law (Electrostatic Force)

Centripetal Force (Circular Motion)

2r

kqQF

r

mvF

2

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

2

2

22

2

2

2

vm

ker

rvmke

r

vm

r

ke

e

e

e

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

2

2

2

2

kerm

nrm

rmn

m

ker

ee

ee

2

22

222

kem

nr

kerm

n

en

e

Bohr Radius

The previous equation can be solved for any principal quantum number you choose; check your answer by solving for n = 1, 2

r1=5.29x10-11m r2=2.12x10-10m These values agree well with the

known size of an atom ~10-10m

Section Review

Page 876 1-8