Relativistic Correction of the Rydberg Formula

The relationship E = −K holds between the energy E and kinetic energy K of the electron constituting a hydrogen atom. If the kinetic energy of the electron is determined based on that relationship, then the energy levels of the hydrogen atom are also determined. In classical quantum theory, there is a formula called the Rydberg formula for calculating the wavelength of a photon emitted by an electron. In this paper, in contrast, the formula for the wavelength of a photon is derived from the relativistic energy levels of a hydrogen atom derived by the author. The results show that, although the Rydberg constant is classically a physical constant, it cannot be regarded as a fundamental physical constant if the theory of relativity is taken into account.

The Two Relativistic Rydberg Formulas of Suto and Haug: Further Comments

In a recent paper, we [1] discussed that Suto [2] has pointed out an interesting relativistic extension of Rydberg’s formula. In that paper, we had slightly misunderstood Suto’s approach, something we will comment on further here. The relativistic Suto formula is actually derived from a theory where the standard relativistic momentum relation is changed. The relativistic Rydberg formula we presented and mistakenly thought was the same as Suto’s formula is, on the other hand, derived to be fully consistent with the standard relativistic energy-momentum relation. Here we will point out the differences between the formulas and correct some errors in our previous paper. The paper should give deeper and better intuition about the Rydberg formula and what it represents.

The Physical Constant Called the Rydberg Constant Does Not Exist

In classical quantum theory, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic formulas for describing natural phenomena. However, relativity is not taken into account in this Rydberg formula for wavelength. If the special theory of relativity is taken into account, R∞ can no longer be regarded as a physical constant. That is, we have continued to conduct experiments to this day in an attempt to determine the value of a physical constant, the Rydberg constant, which does not exist in the natural world.

The Relativistic Rydberg’s Formula in Greater Depth and for Any Atom

K. Suto has recently pointed out an interesting relativistic extension of Rydberg’s formula. Here we also discuss Rydberg’s formula, and offer additional evidence on how one can easily see that it is non-relativistic and therefore a good approximation, at best, when . We also extend the Suto formula to hold for any atom and examine the formula in detail.

Theoretical and Experimental Values for the Rydberg Constant Do Not Match

In many areas of physics and chemistry, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic equations for describing natural phenomena. The Rydberg constant appears in the formula for calculating the wavelengths in the line spectrum emitted from the hydrogen atom. However, this Rydberg wavelength formula is a nonrelativistic formula derived at the level of classical quantum theory. In this paper, the Rydberg formula is rewritten as a wavelength formula taking into account the theory of relativity. When this is done, we come to an unexpected conclusion. What we try to determine by measuring spectra wavelengths is not actually the value of the Rydberg constant R∞ but the value Rn,m of Formula (18). R∞ came into common use in the world of nonrelativistic classical quantum theory. If the theory of relativity is taken into account, R∞ can no longer be regarded as a physical constant. That is, we have continued to conduct experiments to this day in an attempt to determine the value of a physical constant, the Rydberg constant, which does not exist in the natural world.

对氢原子光谱实验的讨论

本文从理论上探讨了人们对氢原子光谱的认识过程，由此提出了现有实验中存在的问题。

基于遗传算法构建巴耳末公式

基于遗传算法构建了巴耳末公式 .通过建立合适的拟合数学模型 ,用计算机对数学模型进行优化 ,使之尽可能反映氢原子实际谱线分布 ,并求出经验常量和拟合公式 ,最后分析了所得结果 .

关于玻尔理论的几点注记

根据玻尔的两个基本假设、里德伯公式与经典力学的有关结果 ,可以导出玻尔半径、里德伯常数的表达式与简化有关椭圆轨道的计算 并说明玻尔理论是一种唯象理论 。

关于方程1/m_1~2-1/n_1~2=1/m_2~2-1/n_2~2=…=1/m_k^2-1/n_k^2的正整数解

文献[1]指出,丢番图方程1m21-1n21=1m22-1n2n=…=1m2k-1n2k,当k≥2时恒有一组正整数解。本文作者证明了这方程在k≥2时恒有无穷多组满足(m1,n1,m2,n2,…,mk,nk)=1的正整数解,但无恒满足(mi,ni)=1(i=1,2,…,k)的正整数解。

波尔氢原子光谱理论的里德伯公式

由波尔氢原子光谱理论的里德伯公式证明了存在谱线可以属于不同的谱线系(即存在同一波长(频率)的谱线可以是不同的能级跃迁辐射产生的),即对任意给定的正整数k,总存在谱线同时属于k个不同的谱线系.

以简明物理法重新发现巴耳末公式

物理学是建造数理模型的科学,是追求简明的科学。查阅包括巴耳末本人等文献,都会用一些已知数字推导出经验公式,虽然经验公式是成功的,但推导手法不够简明,且所用数字令人疑惑,有如先知般预见力,能先得知答案再行推导公式,这在逻辑上有倒果为因推论疑虑,实有碍于物理慨念的建立。本文不借助任何既定数字,而是以未知数并运用物理基本概念,于计算不同波长比时,保留物质元素内蕴表征,只要不被约分消掉,其本性自然显露出来,就能推导出经验公式以及推算巴耳末基数,并加以推广;还提出与里德伯公式的等价证明;最后运用量纲分析揭露此一内蕴物理量的真正本质,其等同于由玻尔模型推导出含多项基本物理常数的里德伯常数,非常适合做为正式教学的一个补充。

创新量纲分析重导玻尔模型能级公式

本研究仅从波长实验数据入手,完全独立于玻尔模型,单靠量纲分析就能推导出其能级公式,展现迥异于玻尔模型的物理图像。本文会将现行量纲分析辅以一套自创手法、两个补充概念、三项物理特性,并针对氢原子物理系统,从不连续光谱波长开始,先以创新法找出氢原子光谱线的规律,接着采用Π定理算出氢原子玻尔半径,然后用瑞利法定出氢原子基态能量,最后重新导出玻尔模型能级公式。一路用不同的量纲分析手法连贯下来,此套方案与概念可用到其他类似的原子物理体系中。

氢原子光谱在三种环境下测定里德伯常数实验结果探讨

通过比较正常实验环境下(弱光)、白炽灯和阳光光照的实验结果,分别测得的里德伯常数为10973935.6507 m^(-1)、10971967.5494 m^(-1)和10971924.9037 m^(-1),与理论给出的里德伯常数均较为吻合。三种环境下计算出的相对误差分别为0.00186%、0.0161%和0.0165%。可以看出,环境因素对氢灯光源产生了细微的影响,在弱光的情况下进行实验观测,有利于消除谱线的压力展宽,从而获得更加准确的里德伯常数测量值。

钠光谱分析中运算方法的改进

本文对近代物理实验项目《钠原子光谱的拍摄与分析》的传统教学内容提出了改进,并将微机引入了实验教学。