🔢 量子数计算器Quantum Number Calculator

使用说明与常见问题How-to & FAQ

「量子数计算器」是什么？What is the Quantum Number Calculator tool?

输入主量子数 n，列出所有允许的角量子数 l、磁量子数 mₗ 范围、轨道名称、轨道数和最多容纳的电子数；也可以检查一组 (n, l, mₗ, mₛ) 是否合法。Enter the principal quantum number n to list the allowed l values, the mₗ range, subshell names, orbital counts and maximum electrons, or check whether a set (n, l, mₗ, mₛ) is allowed.

如何使用「量子数计算器」？How do I use the Quantum Number Calculator tool?

在「量子数计算器」中，填写「模式」、「主量子数 n」、「角量子数 l」、「磁量子数 mₗ」、「自旋 mₛ」等参数，结果会随输入实时计算并显示在下方。In the Quantum Number Calculator: Fill in "Mode", "Principal n", "Angular l", "Magnetic mₗ", "Spin mₛ"; results are recalculated instantly as you type.

四个量子数的规则？What are the rules?

n = 1, 2, 3, …；l = 0 … n − 1（对应 s、p、d、f…）；mₗ = −l … +l；mₛ = +1/2 或 −1/2。每个轨道（一组 n、l、mₗ）最多容纳两个自旋相反的电子（泡利不相容原理）。本工具支持 n = 1–10（已知元素的基态只用到 n ≤ 7）。n = 1, 2, 3, …; l = 0 … n − 1 (s, p, d, f, …); mₗ = −l … +l; mₛ = +1/2 or −1/2. Each orbital (one n, l, mₗ) holds at most two electrons of opposite spin (the Pauli exclusion principle). This tool handles n = 1–10 (ground states of known elements only use n ≤ 7).

第 n 层能容纳多少电子？How many electrons fit in shell n?

2n²：第 1 层 2 个、第 2 层 8 个、第 3 层 18 个、第 4 层 32 个。2n²: 2 in shell 1, 8 in shell 2, 18 in shell 3 and 32 in shell 4.

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「量子数计算器」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Quantum Number Calculator uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「量子数计算器」免费吗？需要注册吗？Is the Quantum Number Calculator free? Do I need an account?

「量子数计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Quantum Number Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.