Chapter 8, Problem 1Q

To determine

The reason why three quantum numbers needed to describe the state of one electron atom.

Answer to Problem 1Q

Three quantum numbers are needed to describe the state of one electron atom because they describe location of electrons.

Explanation of Solution

The location of electrons can be described using quantum number. Quantum numbers describes energy levels of atoms and molecules. Electrons reside at different orbitals. There are three quantum numbers of an electron to describe the state of electron.

The three quantum numbers are:

• Principle quantum number $\left(n\right)$: It has integer value and it shows size of orbital.
• Orbital quantum number $\left(l\right)$ : It is also known as angular quantum number, it shows shape of an orbit or subshell.
• Magnetic quantum number $\left(m_l\right)$ : It shows orientation of orbits in space.

In three dimensional spaces, three co-ordinates are required to represent position of any particle and same results are given by Schrodinger wave equation.

Conclusion:

Thus, three quantum numbers are needed to describe the state of one electron atom because they describe location of electrons.