Quantum Numbers
What does the quantum number n represent?
Principal quantum number = energy level/shell.
What shape describes an s orbital?
Spherical
Formula for total nodes in an orbital?
n – 1
In a hydrogen atom, does a 2p orbital have higher or lower energy than a 1s orbital?
Higher
What does the radial probability function describe?
Probability of finding an electron at a certain distance from the nucleus.
For an orbital with l = 2, what letter represents the orbital type?
d orbital.
How many lobes does a p orbital have?
2
Formula for radial nodes?
n – l – 1
Which transition releases more energy: n = 3 → n = 2 or n = 2 → n = 1?
n = 2 → n = 1 (larger ΔE).
Where is the electron most likely found in the 1s orbital?
Near the nucleus.
What are the possible ml values for a 3p orbital?
–1, 0, +1.
Which orbital has a cloverleaf shape?
d orbital
How many radial nodes does a 3s orbital have?
2
Equation for energy of hydrogen electron in level n?
En = –2.18 × 10⁻¹⁸ J (1/n²).
What is a radial node?
A distance from the nucleus where probability = 0.
How many unique quantum numbers are required to specify an electron?
4 (n, l, ml, ms).
Which orbital type (s, p, d, f) has the most complex shapes?
f orbital
How many angular nodes does a p orbital have?
1
Calculate E for an electron at n = 4.
–2.18E–18 × (1/16) = –1.36E–19 J.
Compare 1s vs. 2s orbital probability near the nucleus.
Both have density near the nucleus, but 2s has a radial node further out.
If n = 4 and l = 3, what is the orbital designation?
4f orbital.
Which orbital shape is important for bonding in organic molecules (like carbon double bonds)?
p orbital (overlap forms π bonds)
A 4d orbital has how many total nodes, and how many are angular?
Total = 3, angular = 2, radial = 1.
Energy released when an electron falls from n = 4 to n = 2?
E₄ = –1.36E–19 J; E₂ = –5.45E–19 J; ΔE = 4.09E–19 J released.
Why does a 2s orbital penetrate closer to the nucleus than a 2p orbital?
2s orbital has electron density closer to the nucleus due to fewer angular nodes → greater penetration → lower energy.