Is it true that for a value of $n$ $n$ (n-principal quantum number), the value of $m_{l}$ $m_l$ ( $m_{l}$ $m_l$ -magnetic quantum number) is equal to $n^{2}$ $n^2$ ? If it is true, can you please explain this to me? Thanks.

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Is it true that for a value of $n$ $n$ (n-principal quantum number), the value of $m_{l}$ $m_l$ ( $m_{l}$ $m_l$ -magnetic quantum number) is equal to $n^{2}$ $n^2$ ? If it is true, can you please explain this to me? Thanks.

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Answer 1 · 2015-07-06T12:29:53

The actual value, no. The number of values, yes.

Explanation:

The relationship between the principal quantum number, $n$ $n$ , and the magnetic quantum number, $m_{l}$ $m_l$ , actually goes through the angular momentum quantum number, $l$ $l$ .

![https://www.boundless.com/chemistry/textbooks/boundless-chemistry-textbook/introduction-to-quantum-theory-7]( useruploads.socratic.org )

The angular momentum quantum number can take any value that ranges from $0$ $0$ to $n - 1$ $n-1$

$l = 0, 1, 2, ... , (n-1)$

The magnetic quantum number can take any value that ranges from $-l$ to $l$

$m_l = -l, ... , -1, 0, 1, ... , l$

If you take into account the possible values of $l$ , the magnetic quantum number can thus have values that range from

$m_l = -(n-1), ..., -1, 0, 1, ..., (n-1)$

So, for example, if $n=2$ , $m_l$ can be equal to

$m_l = 0$ $->$ for $l=0$

and

$m_l = {-1, 0, 1}$ $->$ for $l=1$

As you can see, the individual values of $m_l$ don't even come close to the value of $n^2$ .

However, the total number of values $m_l$ can take, if you take into account the values of $l$ , is indeed equal to $n^2$ .

The magnetic quantum number actually tells you how many orbitals a subshell has. In the above example, if $n=2$ , you get

$n=2$ , $l=0$ , $m_l = 0$ $->$ one 2s-orbital;

${:(n=2, l=1, m_l = -1->2p_x), (n=2, l=1, m_l = 0->2p_y), (n=2, l=1, m_l = 1->2p_z) :}}$ $->$ three 3p-orbitals.

This means that the second energy level has a total of two subshells, the 2s-subshell and the 2p-subshell.

The number of orbitals each subshell contains is given by $m_l$ . The 2s-subshell contains one orbital, since you only have one possible value for $m_l$ .

The 2p-subshell contains 3 orbitals, each denoted by a different value of $m_l$ .

The total number of orbitals in the second energy level is 4, which is equal to $n^2$ .

If you try this with $n=3$ , you'll find that you get a total number of $9$ orbitals

one 3s-orbital;
three 3p-orbitals;
five 3d-orbitals.

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Is it true that for a value of $n$ $n$ (n-principal quantum number), the value of $m_{l}$ $m_l$ ( $m_{l}$ $m_l$ -magnetic quantum number) is equal to $n^{2}$ $n^2$ ? If it is true, can you please explain this to me? Thanks.

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Is it true that for a value of nnn (n-principal quantum number), the value of m_lmlm_l (m_lmlm_l-magnetic quantum number) is equal to n^2n2n^2? If it is true, can you please explain this to me? Thanks.

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Is it true that for a value of $n$ $n$ (n-principal quantum number), the value of $m_{l}$ $m_l$ ( $m_{l}$ $m_l$ -magnetic quantum number) is equal to $n^{2}$ $n^2$ ? If it is true, can you please explain this to me? Thanks.