20.4 量子机械原子能模型

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  量子机械原子能模型

  

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  Erwin Schrödinger (1887 – 1961) was an Austrian physicist who achieved fame for his contributions to quantum mechanics, especially the Schrödinger equation , for which he received the Nobel Prize in 1933. His development of what is known as Schrödinger's was made during the first half of 1926. It came as a result of his dissatisfaction with the quantum condition in Bohr's orbit theory and his belief that atomic spectra should really be determined by some kind of discrete value.
  ::Erwin Schrödinger(1887 - 1961年)是奥地利物理学家,因其对量子力学的贡献而获得名声,特别是1933年获得诺贝尔奖的Schrödinger方程式。 他所谓的Schrödinger的研发是在1926年上半年完成的。 这是因为他对Bohr轨道理论中的量子状况感到不满,并且认为原子光谱应该真正由某种离散价值来决定。

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  The Quantum Mechanical Model of the Atom
  ::原子量子机械模型

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  Most definitions of quantum theory and quantum mechanics offer the same description for both. These definitions essentially describe quantum theory as a theory in which both energy and matter have characteristics of waves under some conditions and characteristics of particles under other conditions.
  ::量子理论和量子力学的大多数定义对两者都有相同的描述。 这些定义基本上将量子理论描述为一种理论,在这种理论中,能源和物质在某些条件下都有波的特征,在其他条件下也有粒子的特征。

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  Quantum theory suggests that energy comes in discrete packages called quanta (or, in the case of electromagnetic radiation , photons ). Quantum theory has some mathematical development, often referred to as quantum mechanics, that offers explanations for the behavior of electrons inside the electron clouds of atoms.
  ::量子理论表明,能量来自叫做夸坦的离散包件(或者,在电磁辐射的情况下,光子 ) 。 量子理论有一些数学发展,通常被称为量子力学,为原子电子云中的电子行为提供了解释。

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  The wave-particle duality of electrons within the electron cloud limits our ability to measure both the energy and the position of an electron simultaneously. The more accurately we measure either the energy or the position of an electron, the less we know about the other. Our fact that we cannot accurately know both the position and the of an electron at the same time causes an inability to predict a trajectory for an electron. Consequently, electron behavior is described differently than the behavior of normal sized particles. The trajectory that we normally associate with macroscopic objects is replaced for electrons in electron clouds, with statistical descriptions that show, not the electron path, but the region where it is most likely to be found. Since it is the electron in the electron cloud of an atom that determines its chemical behavior, the quantum mechanics description of electron configuration is necessary to understanding chemistry.
  ::电子云中电子的波粒二元性限制了我们同时测量电子能量和位置的能力。 我们测量电子的能量或位置的准确度越低,对另一种电子的准确度就越低。 我们无法同时准确了解电子的位置和位置的事实导致无法预测电子的轨迹。 因此,对电子行为描述不同于正常大小粒子的行为。 我们通常与大型物体相联系的轨道被电子云中电子电子电子中的电子所取代, 其统计描述显示的不是电子路径,而是最有可能找到电子的区域。 由于它是决定其化学行为的原子电子云中的电子, 电子配置的量子力学描述对于理解化学是必要的。

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  The most common way to describe electrons in atoms according to quantum mechanics is to solve the Schrodinger equation for the energy states of the electrons within the electron cloud. When the electron is in these states, its energy is well-defined but its position is not. The position is described by a probability distribution map called an orbital .
  ::根据量子力学来描述原子中电子的最常用方式是解开电子云中电子能量状态的施罗德宁格方程式。当电子处于这些状态时,其能量是明确的,但其位置不是。其位置由称为轨道的概率分布图来描述。

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  Schrodinger’s equation is shown below.
  ::Schrodinger的方程式如下所示。

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  $$\begin{array}{r}i\hslash \frac{\mathrm{\partial }}{\mathrm{\partial }t}\psi (r,t)=-\frac{\hslash }{2m}{\mathrm{\nabla }}^2\psi (r,t)+V(r,t)\psi (r,t)\end{array}$$

  
  :r,t)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(r,t)+V(r,t)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\(r,t)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

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  where  $\begin{array}{r}i\end{array}$ is the imaginary number, $\begin{array}{r}\sqrt{-1}\end{array}$
  ::i 是想象中的数, ~ 1

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  $\begin{array}{r}\hslash \end{array}$  is Planck’s constant divided by $\begin{array}{r}2\pi \end{array}$
  ::Planck 的常數除以 2

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  $\begin{array}{r}\psi (r,t)\end{array}$  is the wave function
  :r,t) 是波函数

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  $\begin{array}{r}m\end{array}$  is the mass of the particle
  ::m 是粒子的质量

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  $\begin{array}{r}{\mathrm{\nabla }}^2\end{array}$ is the Laplacian operator, $\begin{array}{r}\frac{{\mathrm{\partial }}^2}{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^2}{\mathrm{\partial }{y}^2}+\frac{{\mathrm{\partial }}^2}{\mathrm{\partial }{z}^2}\end{array}$ (these refer to partial second derivatives)
  ::2是Laplacian 经营人,2x222y222z2(这些指部分的第二衍生物)

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  $\begin{array}{r}V(r,t)\end{array}$  is the influencing the particle
  ::V(r,t)是影响粒子的

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  It should be quite clear that without years of high level mathematics, just seeing the equation is no value at all. Without understanding the math, the equation makes no sense.
  ::应该非常清楚的是,如果没有多年的高水平数学,仅仅看到等式根本就没有价值。 不理解数学,等式就毫无意义。

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  The stable energy levels for an electron in an electron cloud are those that have integer values in three positions in the equation. Schrodinger found that having integer values in these three places in the equation produced a wave function that described a standing wave. These three integers are called quantum numbers and are represented by the letters $\begin{array}{r}n\end{array}$ , $\begin{array}{r}l\end{array}$ , and $\begin{array}{r}m\end{array}$ .
  ::电子云中电子的稳定的能量水平是方程式中三个位置的整数值。 Schrodinger发现方程式中这三个位置的整数值产生一个波函数,描述一个常态波。这三个整数被称为量数数字,用字母n、l和m表示。

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  Solutions to Schrödinger’s equation involve four special numbers called quantum numbers . (Three of the numbers, $\begin{array}{r}n\end{array}$ , $\begin{array}{r}l\end{array}$ , and $\begin{array}{r}m\end{array}$ , come from Schrödinger’s equation, and the fourth one comes from an extension of the theory). These four numbers completely describe the energy of an electron. Each electron has exactly four quantum numbers, and no two electrons have the same four numbers. The statement that no two electrons can have the same four quantum numbers is known as the Pauli exclusion principle .
  ::施罗丁格尔方程式的解决方案涉及四个特殊数字,称为量子数字。 (数字中的三个,n, l,和m,来自施罗丁格尔的方程式,第四个来自理论的延伸 ) 。 这四个数字完全描述了电子的能量。 每个电子都有四个量子数字,而没有两个电子有四个相同的数字。 没有任何两个电子可以拥有相同的四个量子数字的说法被称为保利排斥原则。

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  The principal quantum number, $\begin{array}{r}n\end{array}$ , is a positive integer  $\begin{array}{r}(1,2,3,\dots n)\end{array}$ that indicates the main energy level of an electron within an atom. According to quantum mechanics, every principal energy level has one or more sub-levels within it. The number of sub-levels in a given energy level is equal to the number assigned to that energy level. That is, principal energy level 1 will have 1 sub-level, principal energy level 2 will have two sub-levels, principal energy level 3 will have three sub-levels, and so on. In any energy level, the maximum number of electrons possible is $\begin{array}{r}2n^2\end{array}$ . Therefore, the maximum number of electrons that can occupy the first energy level is $\begin{array}{r}2(2\times 1^2)\end{array}$ . For energy level 2, the maximum number of electrons is $\begin{array}{r}8(2\times 2^2)\end{array}$ , and for the 3rd energy level, the maximum number of electrons is $\begin{array}{r}18(2\times 3^2)\end{array}$ . The Table lists the number of sub-levels and electrons for the first four principal quantum numbers.
  ::主要量子数, n, 是正数整数(1, 2, 3,...n) , 表示原子内电子的主要能量水平。 根据量子力学, 每个主要能源水平在其中有一个或多个子级。 给定能源水平的子级数量等于给定能源水平的数量。 也就是说, 主能源水平 1 将有一个子级, 主能源水平 2 将有两个子级, 主能源水平 3 将有三个子级等等。 在任何能源水平中, 最大电子数量为 2n2 。 因此, 第一个能源水平上的最大电子数量为 2, 2x12 。 能源水平 2, 最高电子数量为 8 ( 2x22 ) , 第三个能源水平上的最大电子数量为 18 ( 2x32 ) 。 表格列出了前四个主要量值的子级和电子数量 。

  Number of Sub-Levels and Electrons by Principal Quantum Number

  Principal Quantum Number	Number of Sub-Levels	Total Number of Electrons
  1	1	2
  2	2	8
  3	3	18
  4	4	32

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  The largest known atom contains slightly more than 100 electrons. Quantum mechanics sets no limit as to how many energy levels exist, but no more than 7 principal energy levels are needed to describe all the electrons of all the known atoms. Each energy level can have as many sub-levels as the principal quantum number, as discussed above, and each sub-level is identified by a letter. Beginning with the lowest energy sub-level, the sub-levels are identified by the letters $\begin{array}{r}s\end{array}$ , $\begin{array}{r}p\end{array}$ , $\begin{array}{r}d\end{array}$ , $\begin{array}{r}f\end{array}$ , $\begin{array}{r}g\end{array}$ , $\begin{array}{r}h\end{array}$ , $\begin{array}{r}i\end{array}$ , and so on. Every energy level will have an  $\begin{array}{r}s\end{array}$ sub-level, but only energy levels 2 and above will have  $\begin{array}{r}p\end{array}$ sub-levels. Similarly,  $\begin{array}{r}d\end{array}$ sub-levels occur in energy level 3 and above, and  $\begin{array}{r}f\end{array}$ sub-levels occur in energy level 4 and above. Energy level 5 could have a fifth sub-energy level named $\begin{array}{r}g\end{array}$ , but all the known atoms can have their electrons described without ever using the  $\begin{array}{r}g\end{array}$ sub-level. Therefore, we often say there are only four sub-energy levels, although theoretically there can be more than four sub-levels.
  ::已知的最大原子含有略多于100个电子。 量子力学对有多少能源水平没有限制, 但不需要超过7个主要能源水平来描述所有已知原子的所有电子。 每个能源水平的子级别可以与上面讨论的首席量子数相同, 并且每个子级别都用一封信标出。 从最低的能源分级开始, 分级由字母 s, p, d, f, g, h, h, i等等确定。 每个能源水平将有一个子级别, 但只有2级以上才有p级。 同样, d 分级出现在3级和3级以上, f 分级出现在能源水平4级和4级以上。 第5级能源分级可能有第5个分级的g, 但是所有已知的原子可以在不使用g分级的情况下用电子来描述。 因此,我们经常说, 每级只有4个子能源水平, 尽管理论上可以有4个子级别以上。

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  The principal energy levels and sub-levels are shown in the following diagram. The principal energy levels and sub-levels that we use to describe electrons are in red. The energy levels and sub-levels in black are theoretically present but are never used for known atoms.
  ::以下图表显示了主要的能源水平和子等级。我们用来描述电子的主要能源水平和子等级是红色的。黑色的能源水平和子等级在理论上是存在的,但从未用于已知原子。

  

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  The sub-energy levels are identified by the azimuthal quantum number, $\begin{array}{r}l\end{array}$ .
  ::亚能量水平由azimuthal量子数编号l确定。

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  When the azimuthal quantum number $\begin{array}{r}l=0\end{array}$ , the sub-level = $\begin{array}{r}s\end{array}$ .
  ::当 azimuthal 量子数 I=0 时, 子等级 = s 。

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  When the azimuthal quantum number $\begin{array}{r}l=1\end{array}$ , the sub-level = $\begin{array}{r}p\end{array}$ .
  ::当 azimuthal 量子数为 I=1 时, 子等级 = p 。

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  When the azimuthal quantum number $\begin{array}{r}l=2\end{array}$ , the sub-level = $\begin{array}{r}d\end{array}$ .
  ::当 azimuthal 量子数为 I=2, 子等级= d 时 。

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  When the azimuthal quantum number $\begin{array}{r}l=3\end{array}$ , the sub-level = $\begin{array}{r}f\end{array}$ .
  ::当 azimuthal 量子值为 I= 3 时, 子等级 = f 。

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  Quantum mechanics also tells us how many orbitals are in each sub-level. In Bohr’s model, an orbit was a circular path that the electron followed around the nucleus . In quantum mechanics, an orbital is defined as an area in the electron cloud where the probability of finding the electron is high. The number of orbitals in an energy level is equal to the square of the principal quantum number. Hence, energy level 1 will have 1 orbital (1 ² ), energy level 2 will have 4 orbitals (2 ² ), energy level 3 will have 9 orbitals (3 ² ), and energy level 4 will have 16 orbitals (4 ² ).
  ::量子力学还告诉我们每个子级有多少轨道。 在 Bohr 的模型中, 轨道是核心周围的电子环绕路径。 在量子力学中, 轨道被定义为电子云中的一个区域, 在那里, 找到电子的概率很高 。 能量水平中的轨道数量相当于主量数的正方形 。 因此, 能源水平 1 将达到 1 个轨道( 12 ) , 能源水平 2 将达到 4 个轨道 ( 22 ) , 能源水平 3 将达到 9 个轨道 ( 32 ) , 能源水平 4 将达到 16 个轨道 ( 42 ) 。

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  The  $\begin{array}{r}s\end{array}$ sub-level has only one orbital. Each of the  $\begin{array}{r}p\end{array}$ sub-levels has three orbitals. The  $\begin{array}{r}d\end{array}$ sub-levels have five orbitals, and the  $\begin{array}{r}f\end{array}$ sub-levels have seven orbitals. If we wished to assign the number of orbitals to the unused sub-levels,  $\begin{array}{r}g\end{array}$ would have nine orbitals and $\begin{array}{r}h\end{array}$  would have eleven. You might note that the number of orbitals in the sub-levels increases by odd numbers $\begin{array}{r}(1,3,5,7,9,11,\dots )\end{array}$ . As a result, the single orbital in energy level 1 is the  $\begin{array}{r}s\end{array}$ orbital. The four orbitals in energy level 2 are a single  $\begin{array}{r}2s\end{array}$ orbital and three  $\begin{array}{r}2p\end{array}$ orbitals. The nine orbitals in energy level 3 are a single  $\begin{array}{r}3s\end{array}$ orbital, three  $\begin{array}{r}3p\end{array}$ orbitals, and five  $\begin{array}{r}3d\end{array}$ orbitals. The sixteen orbitals in energy level 4 are the single  $\begin{array}{r}4s\end{array}$ orbital, three  $\begin{array}{r}4p\end{array}$ orbitals, five  $\begin{array}{r}4d\end{array}$ orbitals, and seven  $\begin{array}{r}4f\end{array}$ orbitals.
  ::分级轨道只有1个轨道。 每一分级的分级有3个轨道。 d分级有5个轨道, f分级有7个轨道。 如果我们想将轨道数分配给未使用的分级, g 将有9个轨道和 h 将有11个轨道。 你可能注意到, 分级的轨道数增加了奇数(1, 5, 7, 9, 11,...) 。 因此, 能源一级中的单一轨道是轨道。 2级的4个轨道是单2个轨道和3个轨道。 3级的9个轨道是单3个轨道, 3个3个轨道, 5个轨道。 4级的16个轨道是单4个轨道, 3个轨道, 5个轨道和7个轨道。

  Principal Energy Level	播放段落 Number of Orbitals Present ::现有轨道数 播放段落 $\begin{array}{r}spdf\end{array}$ ::s p p d f 年 f 年 f 年 f 年 f 年 f 年 f 年 f f 年	Total Number of Orbitals (n 2 )	Maximum Number of Electrons (2n 2 )
  1	$\begin{array}{r}1---\end{array}$	1	2
  2	$\begin{array}{r}13--\end{array}$	4	8
  3	$\begin{array}{r}135-\end{array}$	9	18
  4	$\begin{array}{r}1357\end{array}$	16	32

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  The Table shows the relationship between  $\begin{array}{r}n\end{array}$ (the principal quantum number), the number of orbitals, and the maximum number of electrons in a principal energy level. Theoretically, the number of orbitals and number of electrons continue to increase for higher values of $\begin{array}{r}n\end{array}$ . However, no atom actually has more than 32 electrons in any of its principal levels.
  ::该表显示了n(主量数)、轨道数和主要能源水平最高电子数之间的关系,理论上说,轨道数和电子数继续增加,数值较高为n。 然而,没有任何原子在其任何主要水平上实际上有32个以上的电子。

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  Each orbital will also have a probability pattern that is determined by interpreting Schrödinger’s equation. The 3-dimensional probability pattern for the single orbital in the  $\begin{array}{r}s\end{array}$ sub-level is a sphere. The probability patterns for the three orbitals in the  $\begin{array}{r}p\end{array}$ sub-levels are shown below. The three images on the left show the probability pattern for the three  $\begin{array}{r}p\end{array}$ orbitals in each of the three dimensions. On the far right is an image of all three  $\begin{array}{r}p\end{array}$ orbitals together. These $\begin{array}{r}p\end{array}$ orbitals are said to be shaped like dumbbells (named after the objects lifters use), water wings (named after the floating balloons young children use in the swimming pool), and various other objects.
  ::每个轨道也将有一个概率模式,由Schrödinger的方程式解释而决定。 S子级中单一轨道的三维概率模式是一个球。下面显示P子级中三个轨道的概率模式。左边的三个图象显示了三个维度中三个轨道的概率模式。最右边是所有三个轨道的图象。这些轨道的形状据说是哑铃(以物体升降器命名)、水翼(以游泳池中漂浮的气球幼崽命名)和其他各种物体。

  

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  The probability patterns for the five  $\begin{array}{r}d\end{array}$ orbitals are more complicated and are shown below.
  ::5个轨道的概率模式更为复杂,如下文所示。

  

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  The seven $\begin{array}{r}f\end{array}$ orbitals shown below are even more complicated.
  ::下文所示的7个轨道轨道更为复杂。

  

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  You should keep in mind that no matter how complicated the probability pattern is, each shape represents a single orbital, and the entire probability pattern is the result of the various positions that either one or two electrons can take.
  ::您应该记住,无论概率模式有多复杂,每个形状都代表单一轨道,整个概率模式是一、两个电子可以采取的不同位置的结果。

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  Have you ever wondered if the elements on Earth are the same as in distant galaxies? How would we ever be able to determine that? Launch the Atomic Colors simulation to learn more about how we measure which colors of light are absorbed by the electrons in the atmosphere of distant stars to determine what atoms they are made of:
  ::你有没有想过地球上的元素是否与远方星系中的元素相同?我们如何才能确定这一点?启动原子颜色模拟,以更多地了解我们如何测量远方恒星大气中的电子吸收哪些光的颜色,以确定它们由哪些原子组成:

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  Summary
  ::摘要

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  • Energy comes in discrete packages called quanta.
    ::能量来自离散的包件 叫做夸特
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  • Electrons in the electron cloud of atoms have a limited number of energy levels due to the quantization of energy.
    ::由于能源的量化,原子电子云中的电子能量水平有限。
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  • The most common way to describe electrons in atoms according to quantum mechanics is to solve the Schrodinger equation for the energy states of the electrons within the electron cloud.
    ::根据量子力学来描述原子中电子的最常见方式是解决电子云中电子能量状态的施罗德宁格方程。
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  • When the electron is in these states, its energy is well-defined but the electron position is not.
    ::当电子处于这些状态时,它的能量是明确的,但电子位置不是。
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  • The position is described by a probability distribution map called an orbital.
    ::该位置由称为轨道的概率分布图描述。
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  • Solutions to Schrödinger’s equation involve four special numbers called quantum numbers. (Three of the numbers, $\begin{array}{r}n\end{array}$ , $\begin{array}{r}l\end{array}$ , and $\begin{array}{r}m\end{array}$ , come from Schrödinger’s equation, and the fourth one comes from an extension of the theory.)
    ::解决Schrödinger方程式的办法涉及四个特殊数字,称为量子数字。 (数字中的三个, n, l, 和 m,来自Schrödinger的方程式,第四个来自理论的延伸。 )
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  • These four numbers completely describe the energy of an electron.
    ::这四个数字完全描述了电子的能量。
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  • Each electron has exactly four quantum numbers, and no two electrons have the same four numbers.
    ::每个电子有4个量子数字, 没有两个电子有相同的4个数字。
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  • The principal quantum number, $\begin{array}{r}n\end{array}$ , is a positive integer  $\begin{array}{r}(1,2,3,\dots n)\end{array}$ that indicates the main energy level of an electron within an atom.
    ::本金量数 n 是正整数(1,2,3,...n),表示原子内电子的主要能量水平。

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  Review
  ::回顾

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  1. If we were dealing with an atom that had a total of 20 electrons in its electron cloud, how many of those electrons would have quantum number $\begin{array}{r}n=1\end{array}$ .
     ::如果我们处理一个原子 其电子云中共有20个电子 有多少个电子的量子号是n=1
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  2. What is the total number of electrons in the $\begin{array}{r}p\end{array}$ -orbitals of the second energy level?
     ::第二个能源水平的轨道上的电子总数是多少?
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  3. How many energy levels are necessary to contain the first 10 electrons in an electron cloud?
     ::在电子云中容纳前10个电子需要多少能量水平?

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  Explore More
  ::探索更多

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  Use this resource to answer the questions that follow.
  ::使用此资源回答下面的问题 。

     

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  1. Who first suggested that matter also might exhibit the properties of both particles and waves?
     ::谁先提出此事可能同时显示出粒子和波浪的特性?
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  2. When the concept of describing the trajectory of an electron was given up, what description of the electron replaced it?
     ::当描述电子轨迹的概念被放弃时,电子的什么描述取代了它?
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  3. If the shape of the electron orbital is spherical, how many values are possible for the quantum number $\begin{array}{r}l\end{array}$ ?
     ::如果电子轨道的形状是球形的,那么对于量子数 1 有多少值是可能的?