Name: 普朗克常數與黑體輻射 (Planck's Constant and BlackBody Radiation)
Uploaded: 2024-10-02T10:38:12.000Z
Duration: 8 min 59 s

In this video, we're going to talk about Planck's constant and blackbody radiation.

在本視頻中，我們將討論普朗克常數和黑體輻射。

Now you might be wondering, what is blackbody radiation?

現在你可能想知道，什麼是黑體輻射？

Well, any object with a temperature above 0 Kelvin is going to emit some form of electromagnetic radiation.

任何溫度高於 0 開爾文的物體都會發出某種形式的電磁輻射。

As the temperature increases, the energy of that radiation will increase as well.

隨著溫度的升高，輻射的能量也會增加。

So imagine if you have a metal, and you heat the metal.

是以，想象一下，如果你有一塊金屬，然後加熱這塊金屬。

As the temperature of the metal goes up, eventually, you'll notice that the metal will have a reddish glow to it.

隨著金屬溫度的升高，最終你會發現金屬會發出紅光。

And as you continue to heat up the metal, as the temperature increases, it's going to appear yellow, and then maybe even whitish.

當你繼續加熱金屬時，隨著溫度的升高，金屬會呈現黃色，然後甚至會泛白。

Whenever you increase the temperature of an object, the molecules in that object will vibrate with more energy.

只要物體的溫度升高，物體中的分子就會以更大的能量振動。

And the oscillations of the electric charges in those molecules can emit electromagnetic radiation.

而這些分子中電荷的振盪會發出電磁輻射。

Let's say this is the third energy level.

When an electron in this atom, when it absorbs energy, it can jump to a higher energy level.

當原子中的電子吸收能量時，它可以躍遷到更高的能級。

Now, when that electron returns to its original state, or if it drops to a lower energy level, it's going to emit electromagnetic energy.

現在，當電子恢復到原來的狀態，或者下降到一個較低的能級時，它就會發射電磁能。

And so as these electrons, as they oscillate back and forth, they can absorb and emit electromagnetic energy.

是以，當這些電子來回擺動時，它們可以吸收和發射電磁能。

Now, the energy that is carried by a photon is a multiple of this value, hf.

現在，光子攜帶的能量是這個值 hf 的倍數。

So we're going to put an n, where n is an integer, h is the Planck's constant, f is frequency.

是以，我們要輸入一個 n，其中 n 是整數，h 是普朗克常數，f 是頻率。

The frequency is measured in hertz, or s to the minus 1, and h is Planck's constant, which is 6.626 times 10 to the negative 34 joules times seconds.

頻率的組織、部門是赫茲（或負 1 的 s），h 是普朗克常數，即 10 的 6.626 次方（負 34 焦耳乘以秒）。

Now, this equation tells us something very important, and that is that the energy of a photon is quantized.

現在，這個等式告訴我們一件非常重要的事情，那就是光子的能量是量化的。

It's not continuous, it can only have discrete values.

它不是連續的，只能有離散值。

So it can't be just any value, but it's a multiple of hf.

是以，它不能是任何值，而是 hf 的倍數。

It can be 1hf, it can be 2hf, 3hf, but nothing in between that.

可以是 1hf，也可以是 2hf、3hf，但沒有介於兩者之間的。

So the energy of a photon can only exist in discrete values, it can't take any value.

是以，光子的能量只能以離散值存在，不能取任何值。

So thus we could say that energy is quantized.

是以，我們可以說能量是量子化的。

Calculate the energy of a photon with a frequency of 4 times 10 to the 14 hertz.

計算頻率為 10 的 4 次方到 14 赫茲的光子的能量。

So we could use this formula to get the answer.

是以，我們可以用這個公式得出答案。

So we're only dealing with a single photon, so n is going to be 1.

是以，我們只處理一個光子，所以 n 將是 1。

Planck's constant, that's 6.626 times 10 to the negative 34, and this is joules times seconds.

普朗克常數，即 10 的 6.626 次方到負 34，這是焦耳乘以秒。

The frequency is 4 times 10 to the 14 hertz.

頻率是 10 的 4 倍，即 14 赫茲。

And hertz is seconds to the minus 1, or 1 over seconds.

赫茲是秒到負 1，或 1 超過秒。

And so we can see the unit, seconds, will cancel.

是以，我們可以看到組織、部門 "秒 "將被取消。

And this is going to leave behind the unit joules.

這樣就會留下焦耳這個組織、部門。

And so the energy is going to be 2.65 times 10 to the negative 19 joules.

是以，能量將是 10 的 2.65 倍，即負 19 焦耳。

So that's the energy of this particular photon.

Now what is the energy of a red photon with a wavelength of 700 nanometers?

波長為 700 納米的紅色光子的能量是多少？

Whenever light has a wavelength of about 700 nanometers, it's going to appear red.

只要光的波長在 700 納米左右，就會呈現紅色。

Now, in order to do this one, we need an additional formula.

現在，為了做到這一點，我們需要一個額外的公式。

The wavelength of light times frequency is equal to the speed of light.

So what we need to do first is we need to calculate the frequency.

是以，我們首先需要計算頻率。

The frequency is the speed of light divided by the wavelength.

And the speed of light, which is the same for all types of electromagnetic radiation in a vacuum, is 3 times 10 to the 8 meters per second.

而在真空中，所有類型的電磁輻射的光速都是一樣的，是每秒 8 米的 10 的 3 倍。

The wavelength is 700 nanometers, and a nanometer is 10 to the minus 9 meters.

波長為 700 納米，一納米等於 10 到負 9 米。

是以，組織、部門儀表將被取消。

Giving us the unit 1 over seconds, which is frequency in hertz.

這樣我們就得到了組織、部門 "1 比秒"，也就是頻率（赫茲）。

So 3 times 10 to the 8 divided by 700 times 10 to the negative 9.

是以，10 的 3 次方除以 10 的 700 次方得負 9。

That's going to give us a frequency of 4.286 times 10 to the 14 hertz.

這樣，我們就能得到 10 的 4.286 次方到 14 赫茲的頻率。

Now that we know the frequency, we can calculate the energy of the red photon.

既然知道了頻率，我們就可以計算出紅色光子的能量。

So since we're only dealing with a single photon, and there's one, and then we have Planck's constant.

既然我們只處理一個光子，而且只有一個，那麼我們就有了普朗克常數。

And then we have the frequency, 4.286 times 10 to the 14.

然後是頻率，10 的 4.286 次方到 14。

I'm going to write 1 over seconds for the unit.

So I got 2.84 times 10 to the negative 19 joules.

所以我得到了 2.84 乘以 10 的負 19 焦耳。

So that is the energy of a single red photon.

現在，我們再來解決一個問題。

What is the energy of 5 blue photons with a wavelength of 450 nanometers?

波長為 450 納米的 5 個藍色光子的能量是多少？

So this problem is very similar to number 2.

是以，這個問題與第 2 個問題非常相似。

The only difference is we have an n value of 5.

唯一不同的是，我們的 n 值是 5。

So let's begin by calculating the frequency.

是以，我們先來計算一下頻率。

The frequency is going to be the speed of light divided by the wavelength.

That's 3 times 10 to the 8 meters per second divided by 450 nanometers or 450 times 10 to the negative 9 meters.

即每秒 8 米的 10 的 3 次方除以 450 納米，或 10 的 450 次方除以負 9 米。

So we're going to cancel the unit meters just like we did before.

是以，我們要像之前一樣取消組織、部門儀表。

So this works out to be 6.67 times 10 to the 14 hertz.

是以，10 的 6.67 倍等於 14 赫茲。

So now that we know the frequency, let's calculate the energy of the photon.

既然知道了頻率，我們就來計算光子的能量。

So E is equal to n h f. n is 5 since we're dealing with 5 photons, 5 blue photons. h is always going to be the same, Planck's constant.

所以 E 等於 n h f。n 是 5，因為我們面對的是 5 個光子，5 個藍光子。

So that's just a number you're going to have to commit to memory.

所以，這只是一個你必須記住的數字。

So 6.67 times 10 to the 14 times Planck's constant times 5 will give us this answer.

是以，6.67 乘以 10，再乘以 14 倍普朗克常數乘以 5，就得出了這個答案。

So the energy of the 5 blue photons combined is going to be 2.21 times 10 to the negative 18 joules.

是以，5 個藍色光子的能量總和將是 10 的 2.21 倍，即負 18 焦耳。

 So now you know how to calculate the energy of a single photon or a group of photons if you know the frequency of the photons or their wavelength.

現在您知道了，如果知道光子的頻率或波長，如何計算單個光子或一組光子的能量。