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Chapter 8: Problem 62

Concerning the concept of subshells and orbitals, (a) How many subshells are found in the \(n=3\) level? (b) What are the names of the subshells in the \(n=3\) level? (c) How many orbitals have the values \(n=4\) and \(\ell=3 ?\) (d) How many orbitals have the values \(n=3, \ell=2\) and \(m_{\ell}=-2 ?\) (e) What is the total number of orbitals in the \(n=4\) level?

Short Answer

Expert verified
The answers to the questions are: (a) 3 subshells, (b) They are 3s, 3p, 3d, (c) 7 orbitals, (d) 1 orbital, (e) 16 orbitals.

Step by step solution

01

Determination of Number of Subshells

In quantum mechanics, the number of subshells in a principal energy level 'n' is equal to the value of 'n'. Therefore for \(n=3\), the number of subshells is 3.
02

Naming of Subshells

The subshells in an energy level 'n' are usually designated by the letters s, p, d, f, corresponding to the azimuthal quantum number values of 0, 1, 2, 3 respectively. Hence, for \(n=3\), the subshells are: 3s, 3p and 3d.
03

Number of Orbitals for Given Quantum Numbers

The number of possible orbitals for a given azimuthal quantum number '\ell' is given by '2\ell+1'. For the case \(n=4\), \(\ell=3\), the number of orbitals is \(2*3+1 = 7\).
04

Specific Orbital for Given Quantum Numbers

If specific quantum numbers are given like \(n=3, \ell=2\) and \(m_{\ell}=-2\), it means we are talking about a specific orbital. Therefore, there is 1 orbital corresponding to these values.
05

Total Number of Orbitals in a Given Level

The total number of orbitals in a principle energy level 'n' is given by \(n^2\). So, for \(n=4\), the total number of orbitals is 16.

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Most popular questions from this chapter

If traveling at equal speeds, which of the following matter waves has the longest wavelength? Explain. (a) electron; (b) proton; (c) neutron; (d) \(\alpha\) particle \(\left(\mathrm{He}^{2+}\right)\).

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