Modern Physics
AP Physics 2 Topic 15 9:32 English narration · English + 中文 subtitles burned in
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By nineteen hundred, physics looked finished.
到一九零零年，物理学看起来已经完成了。
Then three experiments broke it.
然后三个实验把它打破。
A hot glowing object gave out the wrong colours.
炽热的物体放出的颜色不对。
Light falling on a metal knocked electrons out, but only if the colour was right, never however bright.
光照在金属上会打出电子，但只有颜色合适才行， 光再亮也没用。
And a glowing gas gave out sharp separate lines, not a smooth rainbow.
发光的气体放出的是一条条分立的亮线，不是平滑的彩虹。
One idea explained all three. Energy does not flow smoothly. <slow>It arrives in packets — in quanta.</slow>
一个想法解释了这三件事：能量不是连续流动的，它是一份一份地到来的。
This is Unit Fifteen: modern physics.
这是第十五单元：近代物理。
We follow that one idea from the photon, into the atom, and down into the nucleus.
我们将沿着这一个想法，从光子出发，走进原子， 再深入原子核。
Start with light.
先从光开始。
A beam of light is a stream of tiny packets called photons.
一束光是一串微小的能量包，叫做光子。
A photon has no mass and no charge, and in empty space every photon travels at the speed of light; through glass or water it moves more slowly.
光子没有质量，也没有电荷；在真空中，每个光子都以光速运动， 在玻璃或水中则走得更慢。
The energy of one photon is Planck's constant times its frequency — the heart of this whole unit.
一个光子的能量等于普朗克常量乘以它的频率。 这一行就是整个单元的核心。
Higher frequency means a more energetic photon.
频率越高，光子的能量越大。
Brighter light is not stronger photons; just more of them.
更亮的光不是光子更强，而只是光子更多。
Let's use it.
我们来用一用。
Orange light has a frequency of five times ten to the fourteen hertz.
橙色光的频率是五乘十的十四次方赫兹。
What energy does one of its photons carry?
它的一个光子带多少能量？
Multiply Planck's constant by the frequency: six point six three times ten to the minus thirty-four, times five times ten to the fourteen. That is three point three times ten to the minus nineteen joules. Written in electronvolts, about two point one.
用普朗克常量乘以频率：六点六三乘十的负三十四次方，乘以五乘十的十四次方， 得到三点三乘十的负十九次方焦耳；换成电子伏特，大约是二点一。
Every visible photon carries a few electronvolts.
每个可见光光子都带几个电子伏特。
Check the colour: wavelength is speed over frequency, six times ten to the minus seven metres — six hundred nanometres, which is orange.
核对颜色：波长等于光速除以频率， 是六乘十的负七次方米，也就是六百纳米，正是橙色。
Now the shock — wave-particle duality.
接下来是令人震惊的一步。
If a wave can behave like a particle, a particle can behave like a wave.
如果波可以表现得像粒子，粒子也可以表现得像波。
de Broglie said that every moving object has a matter wavelength: Planck's constant divided by its momentum.
德布罗意说：每一个运动的物体都有一个波长，等于普朗克常量除以它的动量。
For a football that is absurdly small, far smaller than a nucleus.
对一个足球来说，这个答案小得离谱，比一个原子核还要小得多。
But slow an electron down, and its wavelength grows to the width of an atom, and at that size it diffracts.
但把电子放慢，它的波长就长到一个原子那么宽，在这个尺度上它会发生衍射。
That is the rule: quantum behaviour only shows up when the wavelength is like the system itself.
这就是判据：只有当波长与系统尺度相当时，量子行为才会显现。
Here is the proof: the double-slit experiment.
这就是证据。
Send waves through two narrow slits and they overlap: bright where they arrive in step, dark where they cancel.
让波通过两条窄缝，它们会叠加：同相到达处变亮，反相处相消变暗。
Now fire electrons at the same two slits, one at a time.
现在把电子射向同样的两条缝，一次只发射一个。
Each lands as a single dot, like a bullet.
每个电子都像子弹一样打成一个点。
But leave it running, and the dots slowly build the very same striped pattern.
但让实验一直做下去，这些点会慢慢堆出完全相同的条纹图样。
Zoom into an atom.
放大看一个原子。
A tiny nucleus of protons and neutrons holds almost all the mass, with light electrons around it.
一个很小的原子核由质子和中子组成，几乎占了全部质量， 外面围着很轻的电子。
The number of protons names the element; change the neutrons for an isotope, the electrons for an ion.
质子数决定了元素种类；改变中子数就得到同位素， 改变电子数就得到离子。
The Bohr model pictures the electrons in fixed circular orbits, held in by the electric pull of the nucleus.
玻尔认为电子在固定的圆轨道上运动， 靠原子核的电吸引力拉住。
Why only certain orbits?
为什么只有某些轨道？
Because the electron is also a wave: an orbit survives only if its circumference fits a whole number of wavelengths.
因为电子同时也是波： 只有周长恰好等于整数个波长的轨道才能存在。
Fixed orbits mean discrete energy levels.
轨道固定，能量也就固定。
An atom can only sit on one of its allowed levels, drawn as a ladder.
原子只能处在它允许的某个能级上，画出来就像一架梯子。
To climb, it must swallow a photon whose energy matches the gap exactly.
要往上跳，它必须吸收一个能量正好等于能级差的光子。
To come down, it emits one.
要落下来，它就放出一个光子。
Hydrogen falling from the third level to the second releases one point eight nine electronvolts — the red line you can see.
氢原子从第三能级落到第二能级，放出一点八九电子伏特，那就是你看到的那条红线。
From the ground state it takes thirteen point six electronvolts to free the electron completely: that is the binding energy, and the lowest level always costs the most.
从基态出发，需要十三点六电子伏特才能让电子完全脱离原子：这就是结合能， 而基态所需的能量总是最大的。
Every element has its own ladder, and so its own emission spectrum: a fingerprint you can read across the galaxy.
每种元素都有自己的一架梯子，也就有自己的一组谱线： 这是一份跨越星系也能读懂的指纹。
Back to the glowing object — blackbody radiation.
回到那个发光的物体。
Any warm body radiates a smooth, continuous spectrum whose shape depends only on temperature.
任何温热的物体都会辐射出平滑连续的光谱， 而谱的形状只取决于它的温度。
Heat it up and two things happen.
把它加热，会发生两件事。
It gets brighter very fast: the power goes as the fourth power of the temperature.
第一，它变亮得非常快：辐射功率与温度的四次方成正比。
And the peak slides to shorter wavelengths, so the glow runs from red hot, to white hot, to blue hot.
第二，峰值向更短的波长移动，所以发光颜色从红热变成白热，再变成蓝热。
Classical physics predicted infinite intensity.
经典物理预言强度会趋于无穷大。
Planck fixed it in one stroke, by assuming the energy of light is quantised.
普朗克一举解决了这个问题， 办法就是假设光的能量是量子化的。
Now the experiment that made photons undeniable: the photoelectric effect.
现在看那个让光子无法被否认的实验。
Shine red light on a metal and nothing comes out.
用红光照射金属，什么也出不来。
Brighter red: still nothing, however long you wait.
把光调亮：还是什么都没有，等多久都一样。
Switch to blue, even a dim blue, and electrons come out at once.
换成蓝光，哪怕很暗的蓝光， 电子立刻就出来了。
A wave picture cannot explain that. A packet picture can: one photon frees one electron, and the packet must be big enough.
波动图像解释不了这一点，能量包的图像可以： 一个光子打出一个电子，而这个能量包必须足够大。
Here is the rule.
规则是这样的。
It costs a minimum energy to pull an electron free, and we call that the work function.
把一个电子从金属中拉出来，需要一个最小的能量， 我们把它叫做逸出功。
The electron leaves with whatever is left over: the photon energy minus the work function.
电子带走的是剩下的部分：光子能量减去逸出功。
Below the threshold frequency nothing is left over, however bright the light.
低于截止频率时没有能量剩下，所以无论光多亮都没有电子逸出。
Plot the greatest kinetic energy against frequency and you get a straight line: the gradient is Planck's constant, crossing the axis at the threshold.
把最大动能对频率作图，你会得到一条直线：斜率就是普朗克常量， 与横轴的交点就是截止频率。
Brightness changes how many electrons, never how fast.
光的亮度只改变电子的数目，从不改变它们的快慢。
Your turn.
轮到你了。
Light of frequency eight times ten to the fourteen hertz falls on a metal with a work function of three times ten to the minus nineteen joules.
频率为八乘十的十四次方赫兹的光照在一块金属上， 这块金属的逸出功是三乘十的负十九次方焦耳。
Pause here and try it.
先暂停，自己试一试。
First the photon: Planck's constant times the frequency is five point three times ten to the minus nineteen joules.
先算光子：普朗克常量乘以频率，等于五点三乘十的负十九次方焦耳。
Subtract the work function: two point three times ten to the minus nineteen joules.
减去逸出功，得到二点三乘十的负十九次方焦耳。
And the threshold?
那截止频率呢？
Work function divided by Planck's constant: four point five times ten to the fourteen hertz.
用逸出功除以普朗克常量：四点五乘十的十四次方赫兹。
One more piece of evidence: Compton scattering.
还有一个证据。
Fire a high-energy photon at a loosely held electron, and the two collide like billiard balls.
把一个高能光子射向一个束缚很松的电子，两者像台球一样碰撞。
Energy and momentum are both conserved, so the electron recoils and the photon leaves with less energy and a longer wavelength.
能量和动量都守恒，所以电子被反冲出去，而光子带着更少的能量、更长的波长离开。
The bigger the deflection, the bigger the shift; straight through, nothing changes.
偏折角越大，波长变化就越大；如果直直穿过，就完全没有变化。
A wave cannot behave like this.
波不会有这种行为。
So a photon carries momentum as well as energy, even with no mass.
所以光子虽然没有质量，却既带能量，也带动量。
Now down into the nucleus, held together by the strong force.
现在深入原子核，它靠强相互作用力结合在一起。
Plot the binding energy for each nucleon: the curve peaks near iron.
把每个核子的结合能画出来，曲线在铁附近达到最高点。
Climbing towards that peak releases energy, so joining light nuclei releases energy — fusion, the engine of the Sun. Splitting a heavy nucleus climbs the same hill — fission, the engine of a reactor.
向这个峰爬升就会释放能量：把轻核合并会放出能量，这就是聚变，太阳的引擎； 把重核分裂同样是在爬这座山，这就是裂变，反应堆的引擎。
Either way the products weigh a little less, and the mass lost appears as energy: mass times the speed of light squared.
两种情况下，生成物都比原料略轻一点，而消失的质量以能量的形式出现： 质量乘以光速的平方。
One gram gives about ninety million million joules.
损失一克质量，就释放大约九十万亿焦耳的能量。
An unstable nucleus fixes itself by radioactive decay, and there are four types.
不稳定的原子核通过衰变让自己变稳定，方式有四种。
In alpha decay the nucleus throws out a helium nucleus: the mass number drops by four, the charge by two.
在阿尔法衰变中，原子核甩出一个氦核：质量数减四，电荷减二。
In beta-minus decay a neutron turns into a proton, firing out an electron and an antineutrino.
在贝塔负衰变中，一个中子变成质子，放出一个电子和一个反中微子。
In beta-plus decay a proton turns into a neutron, firing out a positron and a neutrino.
在贝塔正衰变中，一个质子变成中子，放出一个正电子和一个中微子。
In gamma decay only the energy changes: an excited nucleus emits a photon.
在伽马衰变中只有能量改变：激发态的原子核落到低能态，放出一个光子。
And every equation must balance three things: nucleon number, charge, and lepton number.
而每一个衰变方程都必须让三个量守恒：核子数、电荷和轻子数。
When one single nucleus will decay is pure chance; you can never predict it.
单个原子核什么时候衰变完全是随机的，你永远无法预测。
But a large sample is completely predictable.
但是一大堆原子核的行为却完全可以预测。
Count the nuclei, wait one half-life, and half of them are gone.
数一数原子核，等一个半衰期， 就有一半消失了。
Wait another, and half of what is left goes too.
再等一个半衰期，剩下的又少一半。
The number falls along a smooth curve that never quite reaches zero: an exponential set by the decay constant, the natural log of two divided by the half-life.
数目沿着一条平滑的曲线下降，却永远不会真正到达零：这是指数衰减， 由衰变常量决定，而衰变常量等于二的自然对数除以半衰期。
Two quick ones.
两道小题。
A sample has a half-life of eight days: what fraction is left after twenty-four days?
一个样品的半衰期是八天：二十四天后还剩多少比例？
And what does uranium become when it emits an alpha particle?
还有，铀放出一个阿尔法粒子后会变成什么？
Pause and try both.
先暂停，两题都试一试。
Twenty-four divided by eight is three half-lives, so a half, times a half, times a half: one eighth is left, twelve and a half percent.
二十四除以八等于三个半衰期，所以是二分之一，乘二分之一，再乘二分之一， 剩下八分之一，大约百分之十二点五。
Then uranium two hundred and thirty-eight loses four from the mass number and two from the atomic number, giving element ninety, which is thorium.
再看第二题：铀二三八的质量数减四， 原子序数减二，得到九十号元素，也就是钍。
Three marks students throw away.
三个学生常丢的分。
First, brightness and frequency are not the same thing: more photons means more electrons, higher frequency means faster electrons.
第一，亮度和频率不是一回事：光子更多意味着电子更多， 而频率更高才意味着电子更快。
Second, an atom absorbs a photon only when its energy matches a gap exactly — no partial absorption, no change left over.
第二，只有当光子能量正好等于某个能级差时， 原子才会吸收它；没有部分吸收，也没有找零。
Third, balance every decay equation in three columns: nucleon number, charge, and lepton number — antineutrino in beta-minus, neutrino in beta-plus.
第三，每个衰变方程都要按三栏配平：核子数、电荷和轻子数。 贝塔负衰变要写反中微子，贝塔正衰变要写中微子。