quantum numbers examples

📚 Quick Study Guide

⚛️ Principal Quantum Number (n): Determines the energy level of an electron. $n = 1, 2, 3,...$ Higher values mean higher energy and greater distance from the nucleus. orbital. 🧭 Azimuthal Quantum Number (l): Determines the shape of the electron's orbital and has values from 0 to $n-1$. $l = 0$ (s orbital, spherical), $l = 1$ (p orbital, dumbbell-shaped), $l = 2$ (d orbital, more complex shape), $l = 3$ (f orbital, even more complex). 🧲 Magnetic Quantum Number (ml): Determines the orientation of the electron's orbital in space. It can have values from $-l$ to $+l$, including 0. For example, if $l = 1$, $m_l$ can be -1, 0, or +1, corresponding to the three p orbitals ($p_x, p_y, p_z$). ⬆️ Spin Quantum Number (ms): Determines the intrinsic angular momentum of the electron, which is quantized and called spin. It can only have two values: $+1/2$ (spin up) or $-1/2$ (spin down).

Practice Quiz

1. Which quantum number determines the energy level of an electron?
   1. Principal quantum number (n)
   2. Azimuthal quantum number (l)
   3. Magnetic quantum number (ml)
   4. Spin quantum number (ms)
2. What shape is associated with an orbital when the azimuthal quantum number (l) is 0?
   1. Dumbbell
   2. Spherical
   3. Complex
   4. Diffused
3. If the azimuthal quantum number (l) is 2, what are the possible values of the magnetic quantum number (ml)?
   1. -1, 0, +1
   2. 0, 1, 2
   3. -2, -1, 0, +1, +2
   4. -3, -2, -1, 0, +1, +2, +3
4. Which quantum number describes the intrinsic angular momentum of an electron?
   1. Principal quantum number (n)
   2. Azimuthal quantum number (l)
   3. Magnetic quantum number (ml)
   4. Spin quantum number (ms)
5. What are the possible values for the spin quantum number (ms)?
   1. 0 and 1
   2. +1 and -1
   3. +1/2 and -1/2
   4. Any real number
6. An electron has the following quantum numbers: n=3, l=1, ml=0, ms=+1/2. In which orbital is this electron located?
   1. 3s
   2. 3p
   3. 3d
   4. 3f
7. Which set of quantum numbers is NOT allowed?
   1. n=1, l=0, ml=0, ms=+1/2
   2. n=2, l=1, ml=-1, ms=-1/2
   3. n=3, l=2, ml=+3, ms=+1/2
   4. n=4, l=3, ml=0, ms=-1/2