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If $n = 2$ what are the values of quantum number $l$ and $m$?

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Last updated date: 21st Jul 2024
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Answer
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Hint: $n$ is defined as the principal quantum number of the element. The principal quantum number tells us about the size of the element. The greater the principal quantum number, the farther the electron is far from the nucleus.

Complete answer:
The principal quantum number is defined or denoted by n which tells us about the distance from the nucleus.
$l$ can be defined as the orbital angular momentum. This helps us in defining the shape of the orbit and thus tells us about the angular distribution. It is also equal to the number of angular nodes. Now $l$ varies from $0\,to\,n - 1$
 So here we have the value of $n$as two and the value of $l$ would go from
 $
  0\,to\,n - 1 \\
  0\,to\,2 - 1 \\
  \,0\,to\,1 \\
 $
The value of $l$ is dependent on the principal quantum number
Next, we have to calculate $m$ as well
$m$ is defined as the magnetic quantum number. The magnetic quantum number tells us about the number of orbitals within a subshell. The magnetic quantum number also tells us about the orientation of the electrons in the subshell. The value of $m$ depends on the value of orbital angular momentum.
The value of $m$ varies from $ - l\,to\, + l$
This shows that the spin or the orientation of the electron can be in any direction as we have negative values for $m$ as well in this.
Now value of m is
$
   - l\,to\, + l \\
   = - 1\,to\, + 1 \\
 $
Now here we can say that the magnetic quantum number and the orbital angular momentum depends on the principal quantum number.
The value for $l$ is $0\,to\,1$ and the value of $m$ is $ - 1\,to\, + 1$ for value of $n = 2$.

Note:
There is also another quantum number which is called the electron spin quantum number. This number helps us find out the spin of the electron in the subshells. There are only two values, one being positive half and the other being negative of half. The sign tells us about the direction of the electron.