The number of orbitals with n = 5, m_{l} = +2 | vedclass

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(A) For a given principal quantum number $n = 5$,the possible values of azimuthal quantum number $\ell$ are $0, 1, 2, 3, 4$.The magnetic quantum numbe

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$3$

Vedclass · Answer

(A) For a given principal quantum number $n = 5$,the possible values of azimuthal quantum number $\ell$ are $0, 1, 2, 3, 4$.The magnetic quantum number $m_{l}$ ranges from $-\ell$ to $+\ell$ for each $\ell$.We need to find the number of orbitals where $m_{l} = +2$:$1$. For $\ell = 0$ $(5s)$,$m_{l} = 0$.$2$. For $\ell = 1$ $(5p)$,$m_{l} = \{-1, 0, +1\}$.$3$. For $\ell = 2$ $(5d)$,$m_{l} = \{-2, -1, 0, +1, +2\}$. Here,$m_{l} = +2$ is possible ($1$ orbital).$4$. For $\ell = 3$ $(5f)$,$m_{l} = \{-3, -2, -1, 0, +1, +2, +3\}$. Here,$m_{l} = +2$ is possible ($1$ orbital).$5$. For $\ell = 4$ $(5g)$,$m_{l} = \{-4, -3, -2, -1, 0, +1, +2, +3, +4\}$. Here,$m_{l} = +2$ is possible ($1$ orbital).Total number of orbitals with $m_{l} = +2$ is $1 + 1 + 1 = 3$.

The number of orbitals with $n = 5, m_{l} = +2$ is $......$ . (Round off to the Nearest Integer)

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