Chapter 28, Problem 28P

(a)

To determine

The transition $\text{4p}\to \text{3p}$ is allowed or forbidden.

Answer to Problem 28P

The answer is forbidden.

Explanation of Solution

Given info: Transition: $\text{4p}\to \text{3p}$

Formula used:

The principal quantum number $n$ can take on any integer value $\left(1,2,3,\mathrm{...}\right)$ and also, corresponds to the quantum number of the old Bohr Theory.

The orbital quantum number $l$ can take on values from $0$ to $\text{n-1}$ .

Calculation:

In allowed and forbidden transitions only a fraction of all possible transition are observed. Allowed transitions are of high probability, high intensity, and electric dipole interaction whereas, forbidden transitions are of low probability, weak intensity, non-electric dipole interaction.

So, $\text{4p}\to \text{3p}$ transition is forbidden because $\Delta l\ne \pm 1$

(b)

To determine

The transition $\text{2p}\to \text{1s}$ is allowed or forbidden.

Answer to Problem 28P

The answer is allowed.

Explanation of Solution

Given info: Transition: $\text{2p}\to \text{1s}$

Formula used:

The principal quantum number $n$ can take on any integer value $\left(1,2,3,\mathrm{...}\right)$ and also, corresponds to the quantum number of the old Bohr Theory.

The orbital quantum number $l$ can take on values from $0$ to $\text{n-1}$ .

Calculation:

In allowed and forbidden transitions only a fraction of all possible transition are observed. Allowed transitions are of high probability, high intensity, and electric dipole interaction whereas, forbidden transitions are of low probability, weak intensity, non-electric dipole interaction.

So, $\text{2p}\to \text{1s}$ transition is allowed because $\Delta l=-1$

(c)

To determine

The transition $\text{3d}\to \text{2d}$ is allowed or forbidden.

Answer to Problem 28P

The answer is forbidden.

Explanation of Solution

Given info: Transition: $\text{3d}\to \text{2d}$

Formula used:

The principal quantum number $n$ can take on any integer value $\left(1,2,3,\mathrm{...}\right)$ and also, corresponds to the quantum number of the old Bohr Theory.

The orbital quantum number $l$ can take on values from $0$ to $\text{n-1}$ .

Calculation:

In allowed and forbidden transitions only a fraction of all possible transition are observed. Allowed transitions are of high probability, high intensity, and electric dipole interaction whereas, forbidden transitions are of low probability, weak intensity, non-electric dipole interaction.

So, $\text{3d}\to \text{2d}$ transition is forbidden because $\Delta l\ne \pm 1$

(d)

To determine

The transition $\text{4d}\to \text{3s}$ is allowed or forbidden.

Answer to Problem 28P

The answer is forbidden.

Explanation of Solution

Given info: Transition: $\text{4d}\to \text{3s}$

Formula used:

The principal quantum number $n$ can take on any integer value $\left(1,2,3,\mathrm{...}\right)$ and also, corresponds to the quantum number of the old Bohr Theory.

The orbital quantum number $l$ can take on values from $0$ to $\text{n-1}$ .

Calculation:

In allowed and forbidden transitions only a fraction of all possible transition are observed. Allowed transitions are of high probability, high intensity, and electric dipole interaction whereas, forbidden transitions are of low probability, weak intensity, non-electric dipole interaction.

So, $\text{4d}\to \text{3s}$ transition is forbidden because $\Delta l\ne \pm 1$

(e)

To determine

The transition $\text{4s}\to \text{3p}$ is allowed or forbidden.

Answer to Problem 28P

The answer is allowed.

Explanation of Solution

Given info: Transition: $\text{4s}\to \text{3p}$

Formula used:

The principal quantum number $n$ can take on any integer value $\left(1,2,3,\mathrm{...}\right)$ and also, corresponds to the quantum number of the old Bohr Theory.

The orbital quantum number $l$ can take on values from $0$ to $\text{n-1}$ .

Calculation:

In allowed and forbidden transitions only a fraction of all possible transition are observed. Allowed transitions are of high probability, high intensity, and electric dipole interaction whereas, forbidden transitions are of low probability, weak intensity, non-electric dipole interaction.

So, $\text{4s}\to \text{3p}$ transition is allowed because $\Delta l=-1$