Quantum Physics

Angular Momentum Quantum Number

A shell is made up of subshells. Subshells are regions of space where electron “clouds” are allowed to exist, and different subshells actually have different shapes. The first subshell is shaped like a sphere as illustrated in Fig 1.0(s) i.e. you can visualize it as a cloud of electrons surrounding the atomic nucleus in three dimensions. The second subshell consists of two “lobes” joined together at a single point near the atom’s center as shown in Fig 1.0(p). The third subshell typically resembles a set of four “lobes” clustered around the atom’s nucleus (Fig 1.0(d)).

Related: Principal Quantum Number

Valid angular momentum quantum numbers are positive integers like principal quantum numbers, but also include zero. These quantum numbers for electrons are symbolized by the letter l. The number of subshells in a shell is equal to the shell’s principal quantum number. Thus the first shell (n=1) has one subshell, numbered 0; the second shell (n=2) has two subshells, numbered 0 and 1; the third shell (n=3) has three subshells, numbered 0, 1, 2.

Figure 1.0 Orbitals

The previous convention for subshell description used letters rather numbers. In this notation, the first subshell (l=0) was designated s, the second subshell (l=1) was designated p, the third subshell (l=2) was designated d, and the fourth subshell (l=3) designated f. The letters come from the words sharp, principal, diffuse and fundamental.

Fig 1.1 (a) Bohr representation of Silver atom, (b) Subshell representation of Ag with division of shells in to subshells (Angular quantum number l), note this figure doesn’t show the actual position of electrons, but represents energy levels.

Recommended Resource: Quantum Physics For Beginners

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John Mulindi

John has a background in Industrial Instrumentation and Applied Physics as well as Electrical Systems (Light and Heavy current). When he is not working or writing he likes watching football, traveling and reading.

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