# How many electrons can have the quantum number set n=5 and ml=1?

Nov 6, 2015

$\text{8 electrons}$

#### Explanation:

As you know, each electron has a unique set of quantum numbers that describes its exact location in an atom. In your case, you are given two qunatum numbers, $n$, the principal quantum number, and ${m}_{l}$, the *magnetic quantum number, and are sked to determine how many electrons can share these two quantum numbers in an atom.

The principal quantum number describes the energy level, or energy shell, on which the electron resides. Now, notice that the values the magnetic quantum number can take depend on the value of $l$, the angular momentum quantum number.

For an electron that has $n = 5$, $l$ can be

l = {0; 1; 2; 3; 4}

As you can see, the magnetic quantum number can take values from $- l$ all the way up to $l$. If ${m}_{l} = 1$, it follows that $l$ could very easily be

l = { 1; 2; 3; 4}

FInally, the spin quantum number, ${m}_{s}$, which describes the electron's spin, can only take one of two values

m_s = {-1/2; +1/2}

This means that you will have

• n = 5; l=1; m_l = 1: m_s = +- 1/2
• n = 5; l=2; m_l = 1: m_s = +- 1/2
• n = 5; l=3; m_l = 1: m_s = +- 1/2
• n = 5; l=4; m_l = 1: m_s = +- 1/2

SImply put, two electrons of opposite spins can share one orbital (given by ${m}_{l} = 1$) per subshell (given by $l$).

Therefore, total of $8$ electrons that can share those two quantum numbers.