布鲁格利·波浪等分

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Bohr’s model of the was valuable in demonstrating how electrons were capable of absorbing and releasing energy and how were created. However, the model did not really explain why electrons should exist only in fixed circular orbits rather than being able to exist in a limitless number of orbits all with different energies. In order to explain why atomic energy states are quantized, scientists needed to rethink the way in which they viewed the nature of the and its movement.
::伯赫尔的模型在展示电子如何吸收和释放能源以及如何创造能源方面很有价值。 但是,模型并没有真正解释为什么电子应该只存在于固定环绕轨道中,而不是能够存在于数量无限的轨道中,而所有轨道都具有不同的能量。 为了解释为什么原子能国家被量化,科学家需要重新思考他们看待其性质及其运动的方式。

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De Broglie Wave Equation
::Degbrolie 波浪等量

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Planck’s investigation of the emission spectra of hot objects and the subsequent studies into the had proven that light was capable of behaving both as a wave and as a particle. It seemed reasonable to wonder if electrons could also have a dual wave-particle nature. In 1924, French scientist Louis de Broglie (1892-1987) derived an equation that described the wave nature of any particle. Particularly, the wavelength  $\begin{align*}(\lambda)\end{align*}$ of any moving object is given by:
::普朗克(Planck)对热天体排放光谱的调查以及随后对热天体排放光谱的研究证明光线既可以作为波,也可以作为粒子。 似乎有理由怀疑电子是否也可以具有双波粒子的性质。 1924年,法国科学家路易·德布罗格里(Louis de Broglie (1892-1987))得出了一个描述任何粒子波性质的方程。 特别是,任何移动天体的波长()是由以下几个因素提供的:

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$$\begin{align*}\lambda=\frac{h}{mv}\end{align*}$$
::*hmv* * hmv* * hmv* * hmv* * hmv * hmv *hm* *hm* *hmv *hm* *hmv *hmv *hm *hmv *hmv *hmv *hmv *hmv *hmv *hmv *hmmv *hmv *hmv *hmv *hmv *hmv *hmv( hmv) *hmv( hmv) *hmv( hmv) *hmv( hmv)(hmv)

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In this equation,  $\begin{align*}h\end{align*}$ is Planck’s constant,  $\begin{align*}m\end{align*}$ is the mass of the particle in kg, and  $\begin{align*}v\end{align*}$ is the velocity of the particle in m/s. The problem below shows how to calculate the wavelength of the electron.
::在此方程中, h 是 Planck 的常数, m 是以公斤表示的粒子质量, v 是以毫/秒表示的粒子速度。 下面的问题是如何计算电子的波长 。

 

 

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Sample Problem: de Broglie Wave Equation
::抽样问题:broglie波平方

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An electron of mass 9.11 × 10 ^-31 kg moves at nearly the speed of light . Using a velocity of 3.00 × 10 ⁸ m/s, calculate the wavelength of the electron.
::9.11× 10-31公斤质量电子以接近光速移动。使用3.00× 108米/秒的速度计算电子的波长。

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Step 1: List the known quantities and plan the problem.
::第1步:列出已知数量并规划问题。

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Known
::已知已知

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• mass  $\begin{align*}(m)\end{align*}$ = 9.11 × 10 ^-31 kg
  :m) = 9.11 × 10-31公斤
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• Planck's constant  "> $\begin{align*}(h)\end{align*}$ = 6.6262  10 ^-34 × J •  s
  ::普朗克常数 = 6.6262 10-34 × J • s
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• velocity $\begin{align*}(v)\end{align*}$ = 3.00 × 10 ⁸ m/s
  ::速度(五)=3.00×108米/秒

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Unknown
::未知

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• wavelength  $\begin{align*}(\lambda)\end{align*}$
  ::运动波长 (____________________________________________________________________________________________________________________________________________

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Apply the de Broglie wave equation $\begin{align*}\lambda=\frac{h}{mv}\end{align*}$ to solve for the wavelength of the moving electron.
::应用 de Broglie 波方程式 hmv 解答移动电子的波长 。

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Step 2: Calculate.
::第2步:计算。

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$\begin{align*}\lambda=\frac{h}{mv}=\frac{6.626 \times 10^{-34}\ \text{J} \cdot \text{s}}{(9.11 \times 10^{-31} \ \text{kg}) \times (3.00 \times 10^8 \ \text{m/s})}=2.42 \times 10^{-12} \ \text{m}\end{align*}$
::hmv=6.626×10-34 Js(9.11×10-31公斤)×(3.00×108 m/s)=2.42×10-12 m

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Step 3: Think about your result.
::步骤3:想想你的结果。

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This very small wavelength is about 1/20th of the diameter of a hydrogen atom. Looking at the equation, as the speed of the electron decreases, its wavelength increases. The wavelengths of everyday large objects with much greater masses should be very small.
::这个非常小的波长大约是氢原子直径的1/20倍。看这个方程,随着电子速度的下降,其波长会增加。质量大得多的日常大型物体的波长应该非常小。

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If we were to calculate the wavelength of a 0.145 kg baseball thrown at a speed of 40 m/s, we would come up with an extremely short wavelength on the order of 10 ^-34   m. This wavelength is impossible to detect even with advanced scientific equipment. Indeed, while all objects move with wavelike motion, we never notice it because the wavelengths are far too short. On the other hand, particles with measurable wavelengths are all very small. However, the wave nature of the electron proved to be a key development in a new understanding of the nature of the electron. An electron that is confined to a particular space around the nucleus of an atom can only move around that atom in such a way that its electron wave “fits” the size of the atom correctly. This means that the frequencies of electron waves are quantized . Based on the  $\begin{align*}E=hv\end{align*}$ equation, the quantized frequencies means that electrons can only exist in an atom at specific energies, as Bohr had previously theorized.
::如果我们计算出以40米/秒的速度投下的0.145公斤棒球的波长,我们就会得出10-34米的极短波长。即使使用先进的科学设备,这种波长也无法探测。事实上,尽管所有物体都以波状运动移动,但我们从未注意到它,因为波长太短。另一方面,具有可测量波长的粒子都非常小。然而,电子的波性质证明是对电子性质的新认识中的一个关键发展。限制在原子核周围某一空间的电子只能绕着原子移动,其电波“适合”原子的大小。这意味着电波的频率是四分化的。根据E=hv方程式,四分化的频率意味着电子只能存在于特定能量的原子中,正如Bohr先前的理论一样。

  

 

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Summary
::摘要

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• The de Broglie wave equations allows calculation of the wavelength of any moving object.
  ::de Broglie波方程式允许计算任何移动对象的波长。
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• As the speed of the electron decreases, its wavelength increases.
  ::随着电子速度的下降 其波长会增加

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Review
::回顾

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1. What did the Bohr model not explain?
   ::博尔模型没有解释什么?
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2. State the de Broglie wave equation.
   ::州布洛格利波方程式
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3. What happens as the speed of the electron decreases?
   ::当电子速度下降时会怎样?