Photons
A-Level Physics Topic 22 15:44 English narration · English + 中文 subtitles burned in
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Here is a puzzle that broke classical physics.
有一个谜题，曾把经典物理击碎。
Shine the brightest red lamp you can find onto a metal plate.
把你能找到的最亮的红灯照在一块金属板上。
Pour on more and more light.
再加更多、更多的光。
And yet — nothing happens at all.
然而——什么都没发生。
No electrons come out.
没有电子跑出来。
Now switch to a faint blue glow, dimmer than before.
现在换成一束微弱的蓝光， 比刚才还要暗。
Instantly, electrons stream out.
可就在一瞬间，电子喷涌而出。
Brightness did not matter.
亮度不重要。
Colour did.
颜色才重要。
The only way to explain it: light comes in packets, and the colour sets each packet's punch.
唯一能解释它的说法是：光是一份一份地到来的，而颜色决定了每一份的力道。
Light is a wave — but it is also a stream of particles called photons.
光是一种波——但它也是一束叫做光子的粒子流。
Today: the energy of a photon, the photoelectric effect, wave-particle duality, and the energy levels inside atoms.
今天：一个光子的能量、光电效应、 波粒二象性，以及原子内部的能级。
Let's begin.
让我们开始吧。
Light energy comes in lumps, called photons — each a tiny packet of energy, a quantum, and the plural is quanta.
光的能量是一块一块的，叫做光子——每一个都是一小份能量，一个量子。
The energy of one photon is the Planck constant, times its frequency.
一个光子的能量， 等于普朗克常量乘以它的频率。
A higher frequency means a more energetic photon.
频率越高，光子的能量就越大。
And since frequency and wavelength are linked, the shorter the wavelength, the more energy each photon carries.
而由于频率和波长是相连的， 波长越短，每个光子携带的能量就越多。
These energies are tiny, so we measure them in a tiny unit: the electronvolt.
这些能量非常小，所以我们用一个很小的单位来量它： 电子伏特。
Let us use that formula.
我们来用一下这个公式。
Find the energy of one photon of green light of wavelength five hundred nanometres.
求一个波长为五百纳米的绿光光子的能量。
Take Planck's constant as six point six three times ten to the minus thirty-four joule seconds, and the speed of light as three times ten to the eighth metres per second.
取普朗克常量为 六点六三乘以十的负三十四次方焦耳秒，光速为三乘以十的八次方米每秒。
We know the wavelength, not the frequency, so we want E equals h c over lambda.
我们知道的是波长， 不是频率，所以要用 E 等于 h c 除以 lambda。
Put the numbers in, and remember that a nanometre is ten to the minus nine metres, so five hundred nanometres is five times ten to the minus seven metres.
把数字代进去，并记住一纳米是十的负九次方米， 所以五百纳米就是五乘以十的负七次方米。
The answer is four times ten to the minus nineteen joules.
答案是四乘以十的负十九次方焦耳。
That is a tiny number in joules, which is exactly why we also quote it as about two and a half electronvolts.
用焦耳表示是个极小的数，这正是我们也把它写成约二点五电子伏特的原因。
The electronvolt deserves a proper definition, because it is the unit this whole topic lives in.
电子伏特值得给一个正式的定义，因为整个这一章都活在这个单位里。
One electronvolt is the kinetic energy an electron gains when it moves through a potential difference of one volt.
一电子伏特，就是一个电子 通过一伏特电势差时获得的动能。
Because the electron's charge is one point six times ten to the minus nineteen coulombs, one electronvolt is one point six times ten to the minus nineteen joules.
由于电子的电荷是一点六乘以十的负十九次方库仑， 所以一电子伏特等于一点六乘以十的负十九次方焦耳。
So to go from electronvolts to joules you multiply by that number, and to come back you divide.
因此从电子伏特换到焦耳要乘以这个数， 换回来则要除以它。
Why bother?
为什么要费这个事？
Because on the atomic scale the numbers become friendly: a visible photon is about two and a half electronvolts, and the work functions of metals are just two to five electronvolts.
因为在原子尺度上，数字会变得亲切： 一个可见光光子约为二点五电子伏特，而各种金属的逸出功只有二到五电子伏特。
Here is something that sounds impossible.
接下来这件事听上去不可能。
A photon also carries momentum.
光子也带有动量。
Its momentum is p equals E over c, and since E is h c over lambda, that tidies up beautifully to p equals h over lambda.
它的动量是 p 等于 E 除以 c， 而由于 E 等于 h c 除以 lambda，整理之后就漂亮地变成 p 等于 h 除以 lambda。
Now, momentum is usually mass times velocity, and a photon has zero rest mass.
可是动量通常是质量乘以速度，而光子的静止质量为零。
That is the point: momentum does not require rest mass.
这正是关键：动量并不需要静止质量。
A photon has no rest mass at all, yet a perfectly real momentum of E over c.
光子完全没有静止质量，却有一个真实存在的、大小为 E 除以 c 的动量。
And this is measurable.
而且这是可以测量的。
Photons striking a surface push on it, which we call radiation pressure, and it is how a solar sail drives a spacecraft with nothing but sunlight.
光子打在表面上会推它一把，我们称之为辐射压，太阳帆就是靠它，仅用阳光推动飞船。
Watch it happen, photon by photon.
我们一个光子一个光子地看它发生。
Each arriving photon carries one fixed parcel of energy.
每一个到来的光子都带着一份固定的能量。
When a photon meets an electron in the metal, it hands over all of its energy at once — never half, never a slow build-up.
当一个光子遇到金属中的一个电子时，它会一次性把全部能量交出去——绝不会只给一半， 也不会慢慢累积。
If that parcel is big enough, the electron escapes. If it is not, nothing happens, and the next photon starts the story again from the beginning.
如果这一份足够大，电子就逃出来；如果不够，什么也不会发生， 而下一个光子又要从头讲一遍这个故事。
Now the puzzle solved.
现在谜题解开了。
Light hits a metal, and one photon hits one electron, handing over all its energy at once.
光打在金属上，一个光子撞上一个电子，一下子把全部能量交给它。
But it takes a minimum energy just to break an electron free.
但要把一个电子挣脱出来，至少需要一份最小的能量。
So there is a lowest frequency that works — the threshold frequency.
所以存在一个起作用的最低频率—— 极限频率。
Below it, no electron escapes, however bright the light.
低于它，不管光多亮，都没有电子能逃出来。
That minimum energy is called the work function.
那份最小的能量，叫做逸出功。
Above threshold, whatever is left over becomes the electron's kinetic energy — that is Einstein's photoelectric equation.
在极限频率之上，剩下的能量就变成电子的动能——这就是爱因斯坦的光电方程。
You can see this on a bench with a gold-leaf electroscope.
在实验台上用金箔验电器就能看到这一点。
Charge a zinc plate negatively, and the gold leaf lifts and stays lifted, because the leaf and the stem repel each other.
把一块锌板充上负电，金箔会张开并保持张开， 因为箔片和支杆互相排斥。
Now shine ultraviolet light on the plate. The leaf falls.
现在用紫外线照射锌板，金箔就落下来了。
Electrons are being knocked out of the zinc, the plate loses its negative charge, and the repulsion dies away.
电子正被从锌里打出去， 板子失去负电荷，排斥也就消失了。
Shine a bright filament lamp on it instead and the leaf does not move at all — the visible light has plenty of energy arriving, but not enough in any single photon.
可要是换成一盏明亮的白炽灯去照，金箔纹丝不动—— 可见光送来的总能量很多，但任何单个光子的能量都不够。
Every metal has a lowest frequency that will work, called the threshold frequency, f nought.
每种金属都有一个能起作用的最低频率，称为极限频率 f 零。
Below it, no electrons are emitted at all — and this is the crucial word — however bright the light.
低于它，就完全没有电子发射出来—— 而关键的一句话是——无论光有多亮。
You can leave the lamp on all day and get nothing.
你把灯开一整天，也还是什么都得不到。
The energy that matters is the work function, Phi: the least energy needed to free an electron from that surface.
真正起作用的能量是 逸出功 Phi：把一个电子从那个表面释放出来所需的最小能量。
The two are linked by Phi equals h f nought, so the threshold frequency is simply the work function expressed as a frequency.
两者由 Phi 等于 h f 零联系起来， 所以极限频率不过就是用频率表示的逸出功。
Different metals hold their electrons with different strengths, and typical work functions sit between about two and five electronvolts.
不同金属束缚电子的强弱不同， 典型的逸出功在大约二到五电子伏特之间。
Let us put Einstein's equation to work.
我们来用一下爱因斯坦方程。
A metal has a work function of two point zero electronvolts.
某金属的逸出功为二点零电子伏特。
Light made of photons of energy three point five electronvolts shines on it.
用能量为三点五电子伏特的 光子组成的光去照射它。
What is the maximum kinetic energy of the photoelectrons?
光电子的最大动能是多少？
Rearrange Einstein's equation: the maximum kinetic energy is h f minus Phi.
把爱因斯坦方程移项：最大动能等于 h f 减 Phi。
Notice that the electronvolt is doing us a favour here, because both quantities are already in the same unit, so we can simply subtract.
注意电子伏特在这里帮了我们大忙，因为两个量已经是同一个单位，直接相减就行。
Three point five minus two point zero gives one point five electronvolts.
三点五减二点零，得到一点五电子伏特。
If an exam asks for joules, multiply by one point six times ten to the minus nineteen, which gives two point four times ten to the minus nineteen joules. Two calculations come up again and again: photon energy from frequency, and maximum kinetic energy from the work function.
如果考题要求用焦耳，就乘以一点六乘以十的负十九次方， 得到二点四乘以十的负十九次方焦耳。
Plot the electrons' maximum kinetic energy against frequency, and you get a straight line: the maximum kinetic energy depends linearly on frequency, crossing the axis exactly at the threshold.
把电子的最大动能对频率作图，你会得到一条直线，恰好在极限频率处穿过横轴。
The gradient is the Planck constant.
这条线的斜率就是普朗克常量。
Notice: the maximum kinetic energy depends only on the frequency — the colour — not on brightness.
请注意：最大动能只取决于频率——也就是颜色——而不取决于亮度。
So what does brightness do?
那亮度又起什么作用呢？
This is why max KE is fixed but the current grows with brightness: a brighter light of the same colour is simply more photons every second, so more electrons come out.
同样颜色下更亮的光，无非是每秒更多的光子，于是更多的电子跑出来。
Brightness sets the current; frequency sets the energy.
亮度决定电流；频率决定能量。
It is worth being precise about why the wave model fails, because examiners ask for it directly.
值得把波动模型错在哪里说清楚，因为考官会直接考这一点。
The wave model predicts that a brighter beam pours in more energy, so the electrons should come out faster; and that any frequency should work if you wait long enough for the energy to build up.
波动模型预言：越亮的光输入的能量越多， 所以电子应该跑得更快；而且只要等得够久让能量累积起来，任何频率都应该行得通。
Experiment says otherwise, on four counts.
实验的结论恰恰相反，有四条。
First, no emission below the threshold frequency, however bright.
第一，低于极限频率就没有发射，无论多亮。
Second, emission is immediate above it, even for very dim light.
第二， 高于它时发射是立即的，哪怕光非常微弱。
Third, maximum kinetic energy depends on frequency, not on brightness.
第三，最大动能取决于频率，而不是亮度。
Fourth, the number of photoelectrons — and so the current — is what depends on brightness.
第四， 真正取决于亮度的是光电子的数目，也就是电流。
The photon model explains all four in one stroke.
光子模型一举解释了这四条。
Take a brighter beam of the same frequency.
取一束同样频率、但更亮的光。
Brighter means more photons every second — but each one still carries exactly h f.
更亮意味着每秒有更多光子—— 但每一个仍然只带着恰好 h f 的能量。
Since one photon frees one electron, the most any single electron can leave with is h f minus Phi, and that is fixed by the frequency alone.
既然一个光子只释放一个电子，那么任何单个电子 离开时最多带走 h f 减 Phi，而这只由频率决定。
Meanwhile the rate at which electrons leave rises with the number of photons arriving.
与此同时，电子离开的速率会随着到达的 光子数增加而上升。
So doubling the brightness doubles the current, and does not change the maximum kinetic energy by even a fraction.
所以把亮度加倍，电流就加倍，而最大动能则一丝一毫都不会改变。
So light is both wave and particle — this is wave-particle duality.
所以光既是波，又是粒子——这就是波粒二象性。
And here is the twist: if waves can act like particles, then particles can act like waves.
而奇妙的地方在这里：如果波能表现得像粒子， 那么粒子也能表现得像波。
Every moving particle has a de Broglie wavelength — the Planck constant, divided by its momentum.
每一个运动的粒子都有一个德布罗意波长——普朗克常量除以它的动量。
Fire a beam of electrons at a thin crystal lattice, and they spread into the rings of a diffraction pattern — interference between the scattered waves, something only waves can do. That is the wave nature of particles, demonstrated.
把一束电子射向一片薄薄的晶体，它们就散成一圈圈的衍射花样——这是只有波才能做到的事。
Faster electrons have shorter wavelengths, and the rings squeeze closer together.
更快的电子波长更短，圆环就挤得更近。
De Broglie asked a beautifully simple question.
德布罗意提出了一个极其简洁的问题。
If a wave can behave like particles, why should particles not behave like waves?
如果波可以表现得像粒子，那粒子为什么不能表现得像波呢？
So he turned the idea around. The de Broglie hypothesis: any moving particle has a wavelength, lambda equals h over p, where p is its momentum, mass times velocity. Try it on an electron moving at four point nine times ten to the seventh metres per second.
于是他把这个想法反转过来，提出任何运动的粒子都有一个波长：lambda 等于 h 除以 p， 其中 p 是它的动量，即质量乘以速度。
Its momentum comes to four point four six times ten to the minus twenty-three kilogram metres per second, and its wavelength is about one and a half times ten to the minus eleven metres.
拿一个以四点九乘以十的七次方米每秒运动的电子来试试。 它的动量为四点四六乘以十的负二十三次方千克米每秒，波长约为一点五乘以十的负十一次方米。
That is close to the spacing between atoms in a crystal — which is the whole reason this idea could be tested.
这与晶体中原子间距非常接近——而这正是这个想法能够被检验的全部原因。
Here is the experiment that settles it.
下面这个实验一锤定音。
Fire a beam of electrons from an electron gun at a very thin film of graphite, and catch them on a fluorescent screen.
用电子枪把一束电子射向一片极薄的石墨膜，再用荧光屏接住它们。
What appears is not a single spot but a set of concentric bright rings.
屏上出现的不是一个点，而是一组同心的亮环。
Only waves diffract — yet these are electrons.
只有波才会衍射——可这些是电子。
The carbon atoms in the graphite are spaced just right to act as the grating.
石墨中碳原子的间距恰到好处，正好充当了光栅。
And the pattern responds exactly as a wave should: speed the electrons up and their momentum rises, so their de Broglie wavelength shortens, they diffract less, and the rings pull in closer together. Slow them down and the rings spread apart again.
而且这个图样的反应完全符合波的规律： 让电子加速，动量变大，德布罗意波长就变短，衍射变弱，圆环就向内收拢； 让它们慢下来，圆环又重新散开。
One more worked example, and it is a favourite.
再做一道例题，而且是很受欢迎的一道。
An electron is accelerated from rest through two and a half thousand volts.
一个电子从静止开始经过两千五百伏特加速。
Find its de Broglie wavelength.
求它的德布罗意波长。
Start from the energy: its kinetic energy is e V, the charge times the potential difference.
从能量出发：它的动能是 e V，即电荷乘以电势差。
Next we need momentum from kinetic energy, and for a non-relativistic particle p equals the square root of two m E k.
接下来我们需要 由动能求动量，对非相对论粒子，p 等于二 m E k 的平方根。
Substituting gives one tidy formula: lambda equals h over the square root of two m e V.
代入后得到一个整齐的公式： lambda 等于 h 除以二 m e V 的平方根。
Put in the electron mass, the electronic charge and the voltage, and the answer is two point five times ten to the minus eleven metres.
把电子质量、元电荷和电压代进去， 答案是二点五乘以十的负十一次方米。
Once again that is about one atomic spacing, which is why the electrons diffract off graphite.
这又一次大约是一个原子间距， 这正是电子能被石墨衍射的原因。
Finally, inside an atom, electrons can only sit at certain discrete energy levels — never in between.
最后，在原子内部，电子只能停在某些分立的能级上——绝不会停在中间。
When an electron drops down from a higher level to a lower one, it releases the energy difference as a single photon.
当一个电子从高能级掉到低能级时，它把这份能量差作为一个光子释放出来。
Because the levels are fixed, only certain photon energies come out, giving sharp bright lines of colour — the emission spectrum.
因为能级是固定的，只有某些特定的光子能量会发出来，形成一条条尖锐明亮的彩色谱线—— 这就是发射光谱。
Every element has its own unique pattern: a fingerprint of the element, written in light.
每种元素都有自己独一无二的图案：用光写成的元素指纹。
Inside an isolated atom, the electron cannot have just any energy.
在一个孤立原子内部，电子不能具有任意能量。
It can only sit at certain energies, called energy levels, and never in between.
它只能处在某些特定的能量上，称为能级， 中间的值一概不行。
There is a convention that trips people up, so let us be explicit: energies are written as negative, with zero chosen for an electron that has just escaped the atom.
有一个约定常常把人绊倒，我们把它说清楚：能量都写成负值， 而零被规定为电子刚好脱离原子时的能量。
Negative therefore means bound.
所以负号意味着被束缚。
For hydrogen the lowest level, the ground state, is minus thirteen point six electronvolts — the most tightly bound the electron can be.
对氢原子来说， 最低的能级，也就是基态，是负十三点六电子伏特——这是电子被束缚得最紧的状态。
Above it lie the excited states, crowding closer and closer together as they approach zero.
在它上面是各个激发态，越靠近零就挤得越密。
Now the link back to photons.
现在回到光子这条线索上。
When an electron drops from a higher level to a lower one, the atom emits exactly one photon, and that photon's energy h f equals the difference between the two levels, E two minus E one.
当一个电子从较高能级落到较低能级时，原子恰好发出一个光子， 而这个光子的能量 h f 等于两个能级之差，E 二减 E 一。
Watch the signs: both energies are negative, but the higher level is the less negative of the two, so their difference comes out positive, as an energy must.
注意符号：两个能量都是负的， 但较高的那个负得更少，所以它们的差是正的——能量本来就该是正的。
Because only certain jumps exist — each one a transition between two levels — only certain photon energies come out.
由于只存在某些特定的跃迁， 也就只有某些特定的光子能量跑出来。
That is why an emission spectrum is a few sharp bright lines on a dark background rather than a continuous rainbow.
这就是为什么发射光谱是暗背景上的几条明亮细线， 而不是一条连续的彩虹。
Every element has its own ladder of energy levels, so every element emits its own particular set of wavelengths.
每种元素都有自己独特的能级阶梯，因此每种元素也都发出属于自己的一组波长。
Here is the periodic table with each element's box replaced by its real spectrum, and no two are alike.
这里是一张周期表，每个元素的方框都换成了它真实的光谱，没有任何两个是相同的。
This is how we know what stars are made of without ever going there — you photograph the light, measure the wavelengths, and read off which elements are present.
我们正是靠这个才知道恒星是由什么构成的，而根本不必到那里去—— 把星光拍下来，量出波长，就能读出其中有哪些元素。
Run the process backwards and you get the mirror image.
把这个过程反过来，就得到一张镜像的图。
When white light passes through a cool gas, a photon whose energy exactly matches an upward jump between two levels can be absorbed, lifting an electron to a higher level.
当白光穿过一团较冷的气体时， 能量恰好等于两个能级之间某个向上跃迁的光子会被吸收，把电子提到更高的能级。
Those particular wavelengths are removed from the beam.
于是这些特定的波长就从光束中被拿掉了。
So instead of bright lines on black, you see dark lines on a bright background — an absorption spectrum.
所以你看到的不是黑底亮线，而是亮底暗线—— 这就是吸收光谱。
And here is the neat part: the dark lines sit at the same wavelengths as that gas's bright emission lines, because they come from the very same pairs of levels.
妙的地方在于：这些暗线所在的波长，与该气体明亮的发射线完全相同， 因为它们来自同一对能级。
The dark lines in sunlight are cooler gas in the Sun's own atmosphere.
阳光中的暗线，正是太阳自身大气中较冷的气体造成的。
To go from two energy levels to a colour, chain the two equations together.
要从两个能级算出颜色，把两个公式串起来就行。
The photon energy is E two minus E one, and the wavelength of the light emitted is h c divided by that difference.
光子能量是 E 二减 E 一， 而发出的光的波长等于 h c 除以这个差值。
The trap here is units: you must convert electronvolts to joules first, by multiplying by one point six times ten to the minus nineteen, or your wavelength will be out by a factor of a billion.
这里的陷阱是单位：你必须先把电子伏特换成焦耳， 乘以一点六乘以十的负十九次方，否则你的波长会差上十亿倍。
There is a shortcut worth memorising for checking your work — h c is about twelve hundred and forty electronvolt nanometres, so a two-electronvolt jump gives about six hundred and twenty nanometres, which is red.
有一个值得记住、 用来检查答案的捷径——h c 约等于一千二百四十电子伏特纳米，所以一个二电子伏特的跃迁 大约给出六百二十纳米，那是红色。
And a useful sanity check: a bigger jump means a more energetic photon, so a shorter wavelength, moving towards the blue end.
还有一个好用的直觉检验：跃迁越大，光子能量越高， 波长就越短，颜色朝蓝端移动。
Three marks to secure.
三个要拿稳的分。
First, photon energy is Planck times frequency, or Planck times the speed of light over wavelength.
第一，光子能量等于普朗克常量乘以频率，或普朗克常量乘以光速除以波长。
Second, the photoelectric equation: photon energy equals work function plus maximum kinetic energy — below threshold, nothing comes out.
第二，光电方程：光子能量等于逸出功加上最大动能——低于极限频率，什么都不出来。
Third, an emitted photon's energy equals the difference between two energy levels.
第三，发射出的光子能量等于两个能级之间的差。
Master these, and photons are yours.
掌握这些，光子就是你的了。
Two more marks that are routinely thrown away.
还有两分是经常被白白丢掉的。
First, de Broglie gives particles a wavelength, lambda equals h over p — and if a question asks for the evidence, electron diffraction is the evidence, because only a wave can diffract.
第一，德布罗意让粒子也有了波长，lambda 等于 h 除以 p—— 而如果题目问证据是什么，电子衍射就是证据，因为只有波才能发生衍射。
Second, when you are asked what the photoelectric effect demonstrates, the answer they want is that it shows that light is quantised: below the threshold frequency no electrons are emitted whatever the intensity, and that single sentence is often the whole mark.
第二， 当被问到光电效应说明了什么时，他们想要的答案是：它表明光是量子化的—— 低于极限频率时，无论强度多大都没有电子发射，而这一句话往往就是全部的分数。