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Atomic Structure Study Guide (page 2)

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Updated on Sep 24, 2011

Example:

What is the energy release when the hydrogen electron goes from n = 5 to n = 2?

E = 2.18 * 10–18 J = 2.18 * 10–18 J

= – 4.58 * 10–19 J

What is the wavelength of the light needed to remove the hydrogen electron from its ground state?

  • ni = 1 and nf = ∞ (completely removed from the atom)
  • Calculate E:

E = 2.18 * 10–18 J = 2.18 * 10–18 J

= 2.18 * 10–18 J

Note:

  • Calculate the wavelength:

9.11 * 10–8 m = 91.1 nm

Quantum Numbers

Four quantum numbers describe the position and behavior of an electron in an atom: the principal quantum number, the angular momentum quantum number, the magnetic quantum number, and the electron spin quantum number. A branch of physics called quantum mechanics mathematically derives these numbers through the Schrödinger equation.

Principal quantum number ( n)     The principle quantum number is the energy level of the electron given the designation n. The value of n can be any integer (1, 2, 3, 4 . . .) and determines the energy of the orbitals.

Angular momentum quantum number ( l)     The angular momentum is the subshell designation of an electron and describes the shape of the orbital. These subshells are described by the letter l. The possible l values for a particular energy level are 0 to (n – 1). The l values are also given a letter designation. The l value is 0, 1, 2, 3, or 4, and the designation is s, p, d, f, or g.

Magnetic quantum number (ml)     The magnetic quantum number (ml) describes the orbital's orientation in space. For a given l value, ml has integer values from –l to +l. In other words, for the p subshell (l = 1), the ml values are –1, 0, and +1, hence three orbitals.

Electron spin quantum number (ms)     The electron spin quantum number describes the spin of an electron. Magnetic fields have shown that the two electrons in an orbital have equal and opposite spins. The ms values for these spins are and .

Table 9.1 Quantum Numbers

Example:

Are the following possible sets of quantum numbers? Explain.

(1, 1, 1, ); (2, 1, 0, ); (3, 2, 1, 1)

(1, 1, 1,): Not possible. For n = 1, l can only be 0, not 1.

(2, 1, 0, ): Possible.

(3, 2, 1, 1): Not possible. ms can only be or .

  

Practice problems for these concepts can be found at -  Atomic Structure Practice Questions

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