The rule of radius averaging in hydrogen atom

9th Annual Basic Science International Conference 2019

自然科学（总论）

Abdurrouf^1

Department of Physics, Brawijaya University, Jl. Veteran Malang, 65145, Indonesia^1

关键词: Average method;    Energy analysis;    Hydrogen atoms;    Orbital quantum numbers;    Orbital radius;    Orbitals;    Principal quantum numbers;    Root Mean Square;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/546/5/052002/pdf
DOI  :  10.1088/1757-899X/546/5/052002

学科分类：自然科学（综合）

来源: IOP

【 摘 要 】

According to quantum mechanics, electrons do not have a fixed position in an atom, and therefore orbitals have no definite radii. However, electrons have characteristic wave functions from which the radius of their orbits can be calculated or averaged. Depending on the average method, there are three most popular expressions for orbital radius, namely the average radius, the root mean square (rms) radius, and the most probable radius. Unfortunately, for hydrogen atom, none of those three radii is equal to the classical radius, even for large principal quantum numbers called the classical regime. Here, by using energy analysis, we propose a harmonic radius and show that the results well agree with the classical radius for each principal and orbital quantum numbers.