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The smallest allowed value of n is n = 3.

With that in mind, let’s get back to our question: What is the smallest non-zero number? If we only have three digits to spare, the smallest possible number is 0.01. With four digits, it’s 0.001.

Explanation: Well, an electron in the s orbital would mean that the orbital angular momentum quantum number l is 0.

n =4 is the minimum n for which f orbitals exist.

For n = 4, l can have values of 0, 1, 2, and 3. Thus, s, p, d, and f subshells are found in the n = 4 shell of an atom. For l = 0 (the s subshell ), m _{l} can only be 0. Thus, there is only one 4s orbital.

Table of Allowed Quantum Numbers

n | l | Orbital Name |
---|---|---|

4 | 4s | |

1 | 4p | |

2 | 4d | |

3 | 4f |

The three quantum numbers ( n, l, and m) that describe an orbital are integers: 0, 1, 2, 3, and so on. The principal quantum number ( n ) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on. The angular quantum number ( l ) can be any integer between 0 and n – 1.

In atoms, there are a total of four quantum numbers: the principal quantum number (n), the orbital angular momentum quantum number ( l ), the magnetic quantum number (m _{l} ), and the electron spin quantum number (m_{s}).

Intrinsic Spin

Table 1. Atomic Quantum Numbers | ||
---|---|---|

Name | Symbol | Allowed values |

Principal quantum number | n | 1, 2, 3,… |

Angular momentum | l | 0, 1, 2,… n − 1 |

Angular momentum projection | m_{l} |
−l, −l + 1,…, −1, 0, 1,…, l − 1, l (or 0, ±1, ± 2,…, ± l) |

If an atom, ion, or molecule is at the lowest possible energy level, it and its electrons are said to be in the ground state. If it is at a higher energy level, it is said to be excited, or any electrons that have higher energy than the ground state are excited. They are then called degenerate energy levels.

Look at the Periodic Table of Elements and find the element that you want to know the quantum number for. Find the principal number, which denotes the element’s energy, by looking in which period the element is found. For example, sodium is in the third period of the table, so its principal quantum number is 3.

Thus, the sets of quantum numbers for four electrons in the ground state of a neutral beryllium atom are (1,0,0,1/2),( 1,0,0,-1/2),( 2,0,0,1/2) and (2,0,0,-1/2).

Quantum Numbers To completely describe an electron in an atom, four quantum numbers are needed: energy ( n ), angular momentum ( ℓ ), magnetic moment (m _{ℓ} ), and spin (m _{s} ). The first quantum number describes the electron shell, or energy level, of an atom. The dynamics of any quantum system are described by a quantum Hamiltonian (H).

A2. Pauli’s Exclusion Principle states that no two electrons in the same atom can have identical values for all four of their quantum numbers. In other words, (1) no more than two electrons can occupy the same orbital and (2) two electrons in the same orbital must have opposite spins (Figure 46(i) and (ii)). Figure 46.

Orbitals are spaces that have a high probability of containing an electron. The s sublevel has just one orbital, so can contain 2 electrons max. The p sublevel has 3 orbitals, so can contain 6 electrons max. The d sublevel has 5 orbitals, so can contain 10 electrons max.

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