在玻尔理论中是氢原子处于基态时电子绕核运行所作的圆轨道的半径。是氢原子最靠近原子核的电子轨道的半径。是原子物理学中的一种长度单位。常用表示。常用以衡量原子的大小。

尼尔斯·玻尔于1913年提出了原子构造的玻尔模型，其中电子环绕着原子核运转。模型中提及电子只会在特定的几个距离（视能量而定）环绕原子核运转。而最简单的原子──氢原子──只有一个电子轨道，该轨道也是电子可运行的最小轨道，其能量是最小的，从原子核向外找到此轨道的最可能距离就被称为玻尔半径。

[编辑] 数值及定义

根据科学技术数据委员会(CODATA)2002年的数据，玻尔半径的值为5.291772108(18)×10^?11米（即约53皮米或0.53埃格斯特朗）。括号内数字(18)代表最后数位的不确定度。此值能用其他物理常数计算出：

http://upload.wikimedia.org/math/4/a/d/4adc35a07cb146b8a34c4e1fdf2107f6.png

其中：

http://upload.wikimedia.org/math/e/a/e/eae818cd3a83d0832ae93ffc91376f1f.png 为真空电容率

http://upload.wikimedia.org/math/2/2/c/22c1e4c2633d9b563f2c5c1f3ac2f52d.png 为约化普朗克常数

http://upload.wikimedia.org/math/8/a/c/8aca1cebec5e967bdfbb4c6ab8b4f852.png 为电子质量

http://upload.wikimedia.org/math/d/a/a/daa379ae6d08730dd5052a339d73f471.png 为电子电荷

http://upload.wikimedia.org/math/e/2/0/e20b66269882d781ddca343afdcb34e2.png 为真空中光速

http://upload.wikimedia.org/math/a/b/c/abc9cf42f7524af7d95c275bcb2ff600.png 为精细结构常数

[编辑] 物理意义

尽管玻尔模型并没有正确地描述原子，玻尔半径还是保有了它的物理意义，代表着电子云大小的完全量子力学描述。因此玻尔半径常被用于原子物理学。（见原子单位）

要注意的是玻尔半径并没有包括约化质量的 效应，所以在其他包括了约化质量的模型中，并不能准确地等于氢原子电子的轨道半径。这是为了方便而设的：上述方程定义的玻尔半径适用于氢原子以外的其他原 子，而它们的约化质量修正值都不同。如果玻尔半径包括了氢原子的约化质量，就有需要加入一个复杂的修正值来使方程适用于其他原子。

电子的玻尔半径是一组三个互相关联的长度单位中的一个，其他两个是电子的康普顿波长http://upload.wikimedia.org/math/c/a/a/caa10ced88cbea6dc25e5c5a7931cdb2.png及经典电子半径http://upload.wikimedia.org/math/8/f/9/8f95fa3ca045670a349e725ad4b45c68.png。玻尔半径是由电子质量m_e，约化普朗克常数http://upload.wikimedia.org/math/2/2/c/22c1e4c2633d9b563f2c5c1f3ac2f52d.png及电子电荷http://upload.wikimedia.org/math/d/a/a/daa379ae6d08730dd5052a339d73f471.png所得出的。这三个长度单位中的任一个都能用其余两个及精细结构常数http://upload.wikimedia.org/math/a/b/c/abc9cf42f7524af7d95c275bcb2ff600.png表示。

http://upload.wikimedia.org/math/7/b/c/7bcd59a065eeb8036d67f8ee76db081e.png

包括了约化质量效应的玻尔半径能由下列方程求出：

http://upload.wikimedia.org/math/d/1/2/d12ec47d76d4fafe5996a6332832de59.png

其中

http://upload.wikimedia.org/math/f/7/b/f7b83128a7fab465194bb3a8cf9bfc19.png 为质子的康普顿波长

http://upload.wikimedia.org/math/c/a/a/caa10ced88cbea6dc25e5c5a7931cdb2.png 为电子的康普顿波长

http://upload.wikimedia.org/math/a/b/c/abc9cf42f7524af7d95c275bcb2ff600.png 为精细结构常数

在上述方程中，约化质量所产生的效应由增加的康普顿波长表示，即电子及质子的康普顿波长之和。

Bohr radius

From Wikipedia, the free encyclopedia

In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy. In the simplest atom, hydrogen, a single electron orbits the nucleus and its smallest possible orbit, with lowest energy, is called the Bohr radius and is the most likely position of the electron.

According to 2006 CODATA the Bohr radius of hydrogen has a value of 5.2917720859(36) × 10^?11 m (i.e., approximately 53 pm or 0.53 ?ngstr?ms).^[1][2] This value can be computed in terms of other physical constants:

http://upload.wikimedia.org/math/4/a/d/4adc35a07cb146b8a34c4e1fdf2107f6.png

where:

http://upload.wikimedia.org/math/e/a/e/eae818cd3a83d0832ae93ffc91376f1f.png is the permittivity of free space

http://upload.wikimedia.org/math/2/2/c/22c1e4c2633d9b563f2c5c1f3ac2f52d.png is the reduced Planck's constant

http://upload.wikimedia.org/math/8/a/c/8aca1cebec5e967bdfbb4c6ab8b4f852.png is the electron rest mass

http://upload.wikimedia.org/math/d/a/a/daa379ae6d08730dd5052a339d73f471.png is the elementary charge

http://upload.wikimedia.org/math/e/2/0/e20b66269882d781ddca343afdcb34e2.png is the speed of light in vacuum

http://upload.wikimedia.org/math/a/b/c/abc9cf42f7524af7d95c275bcb2ff600.png is the fine structure constant.

While the Bohr model does not correctly describe an atom, the Bohr radius keeps its physical meaning as a characteristic size of the electron cloud in a full quantum-mechanical description. Thus the Bohr radius is often used as a unit in atomic physics. See atomic units.

Note that the definition of Bohr radius does not include the effect of reduced mass, and so it is not precisely equal to the orbital radius of the electron in a hydrogen atom in the more physical model where reduced mass is included. This is done for convenience: the Bohr radius as defined above appears in equations relating to atoms other than hydrogen, where the reduced mass correction is different. If the definition of Bohr radius included the reduced mass of hydrogen, it would be necessary to include a more complex adjustment in equations relating to other atoms.

The Bohr radius of the electron is one of a trio of related units of length, the other two being the Compton wavelength of the electron http://upload.wikimedia.org/math/c/a/a/caa10ced88cbea6dc25e5c5a7931cdb2.png and theclassical electron radius http://upload.wikimedia.org/math/8/f/9/8f95fa3ca045670a349e725ad4b45c68.png. The Bohr radius is built from the electron massm_e, Planck's constant http://upload.wikimedia.org/math/2/2/c/22c1e4c2633d9b563f2c5c1f3ac2f52d.png and the electron charge http://upload.wikimedia.org/math/d/a/a/daa379ae6d08730dd5052a339d73f471.png. The Compton wavelength is built from http://upload.wikimedia.org/math/8/a/c/8aca1cebec5e967bdfbb4c6ab8b4f852.png, http://upload.wikimedia.org/math/2/2/c/22c1e4c2633d9b563f2c5c1f3ac2f52d.png and the speed of light http://upload.wikimedia.org/math/e/2/0/e20b66269882d781ddca343afdcb34e2.png. The classical electron radius is built from http://upload.wikimedia.org/math/8/a/c/8aca1cebec5e967bdfbb4c6ab8b4f852.png, http://upload.wikimedia.org/math/e/2/0/e20b66269882d781ddca343afdcb34e2.png and http://upload.wikimedia.org/math/d/a/a/daa379ae6d08730dd5052a339d73f471.png. Any one of these three lengths can be written in terms of any other using the fine structure constant http://upload.wikimedia.org/math/a/b/c/abc9cf42f7524af7d95c275bcb2ff600.png:

http://upload.wikimedia.org/math/5/8/0/580af9efe1248ae32c71ced527cc7af8.png

The Bohr radius including the effect of reduced mass can be given by the following equation:

http://upload.wikimedia.org/math/b/1/1/b119820ba5bed01214e4d7be749574ef.png

where

http://upload.wikimedia.org/math/f/7/b/f7b83128a7fab465194bb3a8cf9bfc19.png is the Compton wavelength of the proton.

http://upload.wikimedia.org/math/c/a/a/caa10ced88cbea6dc25e5c5a7931cdb2.png is the Compton wavelength of the electron.

http://upload.wikimedia.org/math/a/b/c/abc9cf42f7524af7d95c275bcb2ff600.png is the fine structure constant.

In the above equation, the effect of the reduced mass is achieved by using the increased Compton wavelength, which is just the Compton wavelengths of the electron and the proton added together.