Chapter 2.9, Problem 48AAP

(a)

To determine

The wrong information from given set of information and reason for it.

Answer to Problem 48AAP

The values of $\ell \text{,}{m}_{\ell }$ and name are wrong in given set of information.

Explanation of Solution

Write the expression for subsidiary quantum number.

    $\ell =n-1$                                                                                (I)

Here, the subsidiary quantum number is $\ell$ and principal quantum number is $n$.

Write the expression for magnetic quantum number.

    $m_{\ell }=2\ell -1$                                                                           (II)

Here, the magnetic quantum number is $m_{\ell }$.

Conclusion:

Substitute $3$ for $n$ in Equation (I).

    $\begin{array}{l}\ell =3-1\\ \ell =2\end{array}$

Substitute $2$ for $\ell$ in equation (II).

    $\begin{array}{l}{m}_{\ell }=\left(2\times 2\right)+1\\ m_{\ell }=5\end{array}$

Since the value of $\ell =2$ is $n=3$ and, therefore the name of the orbit is $3d$.

Thus, from the given set of information the values of $\ell \text{,}{m}_{\ell }$ and name are wrong. This is because for principal quantum number $n=3$, the value of subsidiary quantum number will be $2$, the value of magnetic quantum number will be $5$ and will be written as $-2,-1,0,+1,+2$.and the name of the orbit will be $3d$ as $\ell =0$ represents $s$ sub shell, $\ell =1$ represents $p$ sub shell, $\ell =2$ represents $d$ sub shell and $\ell =3$ represents $f$ sub shell.

(b)

To determine

The wrong information from given set of information and reason for it.

Answer to Problem 48AAP

The values of $\ell \text{,}{m}_{\ell }$ and name are wrong in given set of information.

Explanation of Solution

Conclusion:

Substitute $2$ for $n$ in Equation (I).

    $\begin{array}{l}\ell =2-1\\ \ell =1\end{array}$

Substitute $1$ for $\ell$ in equation (II).

    $\begin{array}{l}{m}_{\ell }=\left(2\times 1\right)+1\\ m_{\ell }=3\end{array}$

Since the value of $\ell =1$ is $n=2$ and, therefore the name of the orbit is $2p$.

Thus, from the given set of information the values of $\ell \text{,}{m}_{\ell }$ and name are wrong. This is because for principal quantum number $n=2$, the value of subsidiary quantum number will be $1$, the value of magnetic quantum number will be $3$ and will be written as $-1,0,+1$.and the name of the orbit will be $2p$ as $\ell =0$ represents $s$ sub shell, $\ell =1$ represents $p$ sub shell, $\ell =2$ represents $d$ sub shell and $\ell =3$ represents $f$ sub shell.

(c)

To determine

The wrong information from given set of information and reason for it.

Answer to Problem 48AAP

The values of $\ell \text{,}{m}_{\ell }$ and name are wrong in given set of information.

Explanation of Solution

Conclusion:

Substitute $3$ for $n$ in Equation (I).

    $\begin{array}{l}\ell =3-1\\ \ell =2\end{array}$

Substitute $2$ for $\ell$ in Equation (II).

    $\begin{array}{l}{m}_{\ell }=\left(2\times 2\right)+1\\ m_{\ell }=5\end{array}$

Since the value of $\ell =2$ is $n=3$ and, therefore the name of the orbit is $3d$.

Thus, from the given set of information the values of $\ell \text{,}{m}_{\ell }$ and name are wrong. This is because for principal quantum number $n=3$, the value of subsidiary quantum number will be $2$, the value of magnetic quantum number will be $5$ and will be written as $-2,-1,0,+1,+2$.and the name of the orbit will be $3d$ as $\ell =0$ represents $s$ sub shell, $\ell =1$ represents $p$ sub shell, $\ell =2$ represents $d$ sub shell and $\ell =3$ represents $f$ sub shell.

(d)

To determine

The wrong information from given set of information and reason for it.

Answer to Problem 48AAP

The given set of information the values of $\ell \text{,}{m}_{\ell }$ and name are wrong.

Explanation of Solution

Conclusion:

Substitute $3$ for $n$ in Equation (I).

    $\begin{array}{l}\ell =3-1\\ \ell =2\end{array}$

Substitute $2$ for $\ell$ in Equation (II).

    $\begin{array}{l}{m}_{\ell }=\left(2\times 2\right)+1\\ m_{\ell }=5\end{array}$

Since the value of $\ell =2$ is $n=3$ and, therefore the name of the orbit is $3d$.

Thus, from the given set of information the values of $\ell \text{,}{m}_{\ell }$ and name are wrong. This is because for principal quantum number $n=3$, the value of subsidiary quantum number will be $2$, the value of magnetic quantum number will be $5$ and will be written as $-2,-1,0,+1,+2$.and the name of the orbit will be $3d$ as $\ell =0$ represents $s$ sub shell, $\ell =1$ represents $p$ sub shell, $\ell =2$ represents $d$ sub shell and $\ell =3$ represents $f$ sub shell.