Quantum numbers

What are quantum numbers?

advances in the quantum mechanical model was made to explain new observations of atomic spectra

principal quantum number (n)

• n represents the energy level of a orbital

• EX n=1 → 1st shell

• n² = # of orientations

• 2n² = # of electrons in that shell

secondary quantum number (ℓ)

• ℓ represents the type of subshell orbital

• Sommerfeld noticed that if you looked closer at a bright line spectra some lines were actually made up of 2 or more lines packed together

ℓ = 0

s orbital

ℓ = 1

p orbital

ℓ = 2

d orbital

ℓ = 3

f orbital

magnetic quantum number (m_ℓ)

• m_{\ell} represents the # of different orientations of each subshell

• Zeeman noticed that when a strong magnetic field was put near an element its bright line spectrum lines split

• proposed that each type of subshell orbital had different orientations in space

how do you calculate m_ℓ ?

-ℓ to +ℓ (possible values)

magnetic spin (m_s)

• m_s represents the electron spin in each orbital

• 2 electron per orbital

• one electron spins clockwise, other spins counter-clockwise

what does m_s = +1/2 mean?

unpaired electron

what does m_s = -1/2 mean?

paired electron