---
title: "Franck–Hertz：下降的电流能证明什么"
description: "为什么少收集到电子，会揭示原子的激发能？"
canonical_url: "https://sandboxphysics.com/zh/stories/quantum-evidence/franck-hertz-discrete-excitation/"
language: "zh-CN"
page_type: "story"
alternate_languages:
  en: "https://sandboxphysics.com/stories/quantum-evidence/franck-hertz-discrete-excitation/"
last_modified: "2026-10-15"
---

[量子物理：读懂证据](https://sandboxphysics.com/zh/stories/quantum-evidence/)

诺奖 A · 证据与操控

# Franck–Hertz：下降的电流能证明什么

Sandbox Physics · 2026-10-15

为什么少收集到电子，会揭示原子的激发能？

## 仪器测到的是电流

电子在汞蒸气中加速，剩下的能量够越过减速区，才能到达收集极。当年记录的是电流随电压的变化，能级是从这条曲线推出来的。Franck 在诺奖演讲中，把约 4.9 电子伏的特征能量损失和约 253.7 纳米的紫外发射联系起来。

电子发生非弹性碰撞后，剩下的动能可能不够被收集，电流下降就可能说明有能量交给了原子。电子并没有消失，也不是每次碰撞都是非弹性的。碰撞发生在哪里、收集门槛在哪里，都会影响读数。

证据阅读：J. Franck, Nobel lecture (1926): Transformations of kinetic energy of free electrons into excitation energy of atoms

## 间隔比单个电压更有用

加速电压再升高，电子激发一个原子后可以重新获得动能，在被收集前再激发另一个。电流结构于是重复出现，重复的间隔可以对应一个特征能量。读教学模型时可用下式：它把正的元电荷、对应特征之间的电压间隔和激发能近似联系起来。

这只是近似的能量关系，没有拟合数字化的历史数据。接触电势会让电压零点看起来偏移；能量展宽、蒸气密度、弹性散射和减速场都会改变曲线。第一个谷的位置不能单独当成激发能的绝对测量，还要看多个特征之间的间隔是否一致。

$$
\Delta E\approx e\,\Delta V
$$

证据阅读：G. Hertz, Nobel lecture (1926): The results of the electron-impact tests in the light of Bohr’s theory of atoms

## 激发不等于电离

Hertz 在 1968 年回忆，起初他们把现象解释为电离，后来才改正。原子吸收能量后可以仍是中性；把电子移走是另一回事。这段历史说明，测到阈值和正确理解阈值并不是同一件事。Hertz 还提到，有一个更低的亚稳态，激发概率较小，在当时条件下不明显。所以，最突出的间隔并不是汞的最小激发能。

Franck 的演讲拿碰撞能量和一条特定的紫外谱线比较；Hertz 的演讲把电子碰撞结果和玻尔定态联系起来。1925 年的奖项表彰的是电子碰撞原子的规律，演讲在 1926 年发表。实验、后来的解释、获奖年份和演讲日期，要分开来看。

证据阅读：G. Hertz (1968), Memories of James Franck and the electron scattering experiments — Lindau recording and transcript J. Franck, Nobel lecture (1926): Transformations of kinetic energy of free electrons into excitation energy of atoms G. Hertz, Nobel lecture (1926): The results of the electron-impact tests in the light of Bohr’s theory of atoms Nobel Prize in Physics 1925 — official award record

## 证据排除了什么

激发能可以重复测到，这和一种看法相冲突：原子内能可以接收任意小份的能量，没有特定阈值。碰撞得到的能量又和辐射吻合，电学测量和光学测量互相印证。比起单纯看到曲线上有个谷，这样的论证更有说服力。

它不证明电子真的沿轨道绕核转，给不出汞的完整能级图，也不说明装置里没有任何经典效应。要检验另一种解释，就要求它在扣除仪器效应后，同时预言间隔以及间隔和光谱的关系。当年的成功靠的是这些具体检验，一条曲线证明不了普遍结论。

证据阅读：J. Franck, Nobel lecture (1926): Transformations of kinetic energy of free electrons into excitation energy of atoms G. Hertz, Nobel lecture (1926): The results of the electron-impact tests in the light of Bohr’s theory of atoms

## Lab 是模拟，不是历史数据

在激发 Lab 里扫描加速电压，保留收集电流曲线，比较相邻几个谷。调整装置参数，看推出的间隔是不是比第一个谷的位置更稳定。这条曲线是模拟数据，不是 1914 年实验的数字化原始数据。

氢原子 Lab 提供另一种光谱比较。光电发射分析仪把能量问题反过来：入射光把电子从材料里打出来，能量平衡里要算上功函数。它的功函数和显示的动能，都不能拿来代替汞的激发阈值。三个页面共通的是方法，不是同一个样品，也不是同一组历史数据。

证据阅读：N. Bohr (1913), On the Constitution of Atoms and Molecules, Part I, §§1–3 J. Franck, Nobel lecture (1926): Transformations of kinetic energy of free electrons into excitation energy of atoms

## 接着操作模型

下面这些教学 Lab 产生的是模拟数据，和上文讨论的历史观测不是一回事。

- [扫描电子碰撞激发](https://sandboxphysics.com/zh/labs/franck-hertz-excitation/)
- [比较原子谱](https://sandboxphysics.com/zh/labs/hydrogen-orbitals-spectra/)
- [比较光电发射的能量账](https://sandboxphysics.com/zh/labs/photoemission-analyzer/)

## 来源与阅读说明

玻尔的论文和 Hertz 回忆演讲的文字稿都能直接读到。诺奖演讲的 PDF 列作延伸阅读；编写时直接下载返回了 HTTP 403。本文没有复制或数字化任何历史曲线。

1. [N. Bohr (1913), On the Constitution of Atoms and Molecules, Part I, §§1–3](https://www.gutenberg.org/cache/epub/72787/pg72787-images.html)
2. [J. Franck, Nobel lecture (1926): Transformations of kinetic energy of free electrons into excitation energy of atoms](https://www.nobelprize.org/uploads/2018/06/franck-lecture.pdf)
3. [G. Hertz, Nobel lecture (1926): The results of the electron-impact tests in the light of Bohr’s theory of atoms](https://www.nobelprize.org/uploads/2018/06/hertz-lecture.pdf)
4. [G. Hertz (1968), Memories of James Franck and the electron scattering experiments — Lindau recording and transcript](https://mediatheque.lindau-nobel.org/recordings/31437/memories-of-james-franck-and-the-electron-scattering-experiments-german-presentation-1968)
5. [Nobel Prize in Physics 1925 — official award record](https://www.nobelprize.org/prizes/physics/1925/summary/)

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