Question

current attempt in progress
how many orbitals exist in the fourth principal energy level?
there are orbitals in fourth principal energy level.
what is the distribution of these energy levels?
ins, in p, in d, and inf.
in which period are each of these energy levels filled?
the 4s orbital is filled in the, the 4p orbitals are filled in the, the 4d orbitals are filled in the and the 4f orbitals are filled in the.

Explanation:

Step1: Calculate the number of orbitals in the fourth principal energy level

The formula for the number of orbitals in a principal energy level \(n\) is \(n^{2}\). For \(n = 4\), we have \(4^{2}=16\).

Step2: Determine the number of orbitals in \(s\), \(p\), \(d\), and \(f\) sub - levels

• For \(s\) sub - level (\(l = 0\)), the number of orbitals is \(2l + 1=1\).
• For \(p\) sub - level (\(l = 1\)), the number of orbitals is \(2l + 1 = 3\).
• For \(d\) sub - level (\(l = 2\)), the number of orbitals is \(2l+1 = 5\).
• For \(f\) sub - level (\(l = 3\)), the number of orbitals is \(2l + 1=7\).

Step3: Identify the periods in which the orbitals are filled

• The \(4s\) orbital is filled in the fourth period.
• The \(4p\) orbitals are filled in the fourth period.
• The \(4d\) orbitals are filled in the fifth period.
• The \(4f\) orbitals are filled in the sixth period.

Answer:

There are \(16\) orbitals in the fourth principal energy level.
The distribution is \(1\) in \(s\), \(3\) in \(p\), \(5\) in \(d\), and \(7\) in \(f\).
The \(4s\) orbital is filled in the fourth period, the \(4p\) orbitals are filled in the fourth period, the \(4d\) orbitals are filled in the fifth period, and the \(4f\) orbitals are filled in the sixth period.