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Chapter 7: Problem 65

Make a chart of all allowable orbitals in the first four principal energy levels of the hydrogen atom. Designate each by type (for example, \(s, p\) ) and indicate how many orbitals of each type there are.

Short Answer

Expert verified
Energy level 1 has 1s (2 electrons total). Energy level 2 has 2s (2 electrons) and 2p (6 electrons). Energy level 3 has 3s (2 electrons), 3p (6 electrons) and 3d (10 electrons). Energy level 4 has 4s (2 electrons), 4p (6 electrons), 4d (10 electrons) and 4f (14 electrons).

Step by step solution

01

Orbitals in The First Energy Level

In the first energy level (n=1), there is only one type of orbital that exists: 1s. There’s only one 1s orbital, it can hold up to 2 electrons.
02

Orbitals in The Second Energy Level

In the second energy level (n=2), there are two types of orbitals: 2s and 2p. There’s one 2s orbital which can hold up to 2 electrons and there are three orbitals in the 2p sublevel (2px, 2py, 2pz). Each p orbital can hold up to 2 electrons, so that's 6 electrons total in the 2p sublevel.
03

Orbitals in The Third Energy Level

In the third energy level (n=3), there are three types of orbitals: 3s, 3p, and 3d. There’s one 3s orbital which can hold up to 2 electrons; three orbitals in the 3p sublevel (3px, 3py, 3pz) capable of holding 6 electrons total; and the 3d sublevel contains 5 d orbitals (3dxy, 3dxz, 3dyz, 3dx2-y2, 3dz2) which can hold 10 electrons total.
04

Orbitals in The Fourth Energy Level

In the fourth energy level (n=4), there are four types of orbitals: 4s, 4p, 4d, and 4f. There’s one 4s orbital which can hold up to 2 electrons; three orbitals in the 4p sublevel (4px, 4py, 4pz) capable of holding 6 electrons total; five orbitals in the 4d sublevel (4dxy, 4dxz, 4dyz, 4dx2-y2, 4dz2) capable of holding 10 electrons total; and seven orbitals in the 4f sublevel (4fxxx, 4fyyy, etc.) which can hold a total of fourteen electrons.

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Most popular questions from this chapter

Write the ground-state electron configurations for the following elements: Ge, \(\mathrm{Fe}, \mathrm{Zn}, \mathrm{Ni}, \mathrm{W}, \mathrm{Tl}\).

Which of the following species has the most unpaired electrons? \(\mathrm{S}^{+}, \mathrm{S},\) or \(\mathrm{S}^{-}\). Explain how you arrive at your answer.

Which of the four quantum numbers \(\left(n, \ell, m_{\ell}, m_{s}\right)\) determine (a) the energy of an electron in a hydrogen atom and in a many- electron atom, (b) the size of an orbital, (c) the shape of an orbital, (d) the orientation of an orbital in space?

The UV light that is responsible for tanning the skin falls in the 320 - to 400 -nm region. Calculate the total energy (in joules) absorbed by a person exposed to this radiation for \(2.0 \mathrm{~h}\), given that there are \(2.0 \times\) \(10^{16}\) photons hitting Earth's surface per square centimeter per second over a \(80-\mathrm{nm}(320 \mathrm{nm}\) to \(400 \mathrm{nm})\) range and that the exposed body area is \(0.45 \mathrm{~m}^{2}\). Assume that only half of the radiation is absorbed and the other half is reflected by the body. (Hint: Use an average wavelength of \(360 \mathrm{nm}\) in calculating the energy of a photon.)

Identify the following individuals and their contributions to the development of quantum theory: Bohr, de Broglie, Einstein, Planck, Heisenberg, Schrödinger.
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