How many orbitals are present in the n=5 shell of an atom?

• A. 25
• B. 25
• C. 10
• D. 9

Answer: (A)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) defines the shell or energy level of an atom. For a given \(n\), the possible values of the azimuthal quantum number \(l\) range from \(0\) to \(n-1\).
2. For each value of \(l\), the number of orbitals is given by the magnetic quantum number \(m_l\), which ranges from \(-l\) to \(+l\). Therefore, the number of orbitals for each \(l\) is \$2l + 1$.
3. List all possible \(l\) values for \(n=5\): \(l = 0, 1, 2, 3, 4\).
4. Calculate the number of orbitals for each \(l\): for \(l=0\), orbitals = \(1\); for \(l=1\), orbitals = \(3\); for \(l=2\), orbitals = \(5\); for \(l=3\), orbitals = \(7\); for \(l=4\), orbitals = \(9\).
5. Sum all orbitals: \$1 + 3 + 5 + 7 + 9\( to find the total number of orbitals in the \)n=5$ shell.