Chapter 12, Problem 129AE

(a)

Interpretation Introduction

Interpretation:Quantum number that dependson energy of electron for one electron atom should be determined.

Concept introduction:Energy, size, shape, and orientation of atomic orbital are determined with help of some numbers. These numbers are called quantum numbers and are obtained from solution of Schrodinger equation of hydrogen atom by application of boundary conditions.

Below mentioned are four quantum numbers.

1. Principal Quantum Number

It is represented by $n$ . This quantum number is related to size and energy of different atomic orbitals. With increase in value of $n$ , size of orbital becomes larger and electron is present farther from atomic nucleus for longer time.

2. Angular Momentum Quantum Number

It is represented by $l$ . It describes angular momentum of electron in any specific atomic orbital. Shape of orbitals is determined by this quantum number. It can have integral values from 0 to $\left(n-1\right)$ .

Designation of orbitals on basis of different $l$ values is as follows:

  $\begin{array}{ccccc}\text{Value of }l& 0& 1& 2& 3\\ \text{Orbital}& s& p& d& f\end{array}$

3. Magnetic Quantum Number

This quantum number is denoted by $m_l$ . It describes orientation of angular momentum associated with atomic orbital. Its value ranges from $-l$ to $+l$ . Total values of magnetic quantum number is governed by $2l+1$

4. Spin Quantum Number

This quantum number is represented by $m_s$ . It indicates direction of electron spin. It can either $+\frac{1}{2}$ or $-\frac{1}{2}$ .

(b)

Interpretation Introduction

Interpretation:Quantum number that depends on energy of electron of more than one electron atom should be determined.

Concept introduction:Energy, size, shape, and orientation of atomic orbital are determined with help of some numbers. These numbers are called quantum numbers and are obtained from solution of Schrodinger equation of hydrogen atom by application of boundary conditions.

Below mentioned are four quantum numbers.

1. Principal Quantum Number

It is represented by $n$ . This quantum number is related to size and energy of different atomic orbitals. With increase in value of $n$ , size of orbital becomes larger and electron is present farther from atomic nucleus for longer time.

2. Angular Momentum Quantum Number

It is represented by $l$ . It describes angular momentum of electron in any specific atomic orbital. Shape of orbitals is determined by this quantum number. It can have integral values from 0 to $\left(n-1\right)$ .

Designation of orbitals on basis of different $l$ values is as follows:

  $\begin{array}{ccccc}\text{Value of }l& 0& 1& 2& 3\\ \text{Orbital}& s& p& d& f\end{array}$

3. Magnetic Quantum Number

This quantum number is denoted by $m_l$ . It describes orientation of angular momentum associated with atomic orbital. Its value ranges from $-l$ to $+l$ . Total values of magnetic quantum number is governed by $2l+1$

4. Spin Quantum Number

This quantum number is represented by $m_s$ . It indicates direction of electron spin. It can either $+\frac{1}{2}$ or $-\frac{1}{2}$ .