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Planck's Constant - Planck's Constant

Teacher/Instructor Jonathan Osbourne
Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

Planck's constant, abbreviated h, is the ratio of photon energy to the frequency. Planck's constant is used in the blackbody radiation spectrum, which indicates that energy is carried by light in discrete amounts. Planck's constant is also used when calculating the photoelectric effect.

So let's talk about Planck's constant. What is Planck's constant? Well, Planck's constant is a number that comes out of measurements of the blackbody radiation spectrum. So, the blackbody radiation spectrum indicates that if you've got light with a certain frequency, that, the energy that's carried by that light can only be carried in discreet multiples of h times f where this h is Planck's constant and again we measure that form experiment. Form the blackbody radiation spectrum, we fit the data to the experimental or to the theoretical curve that Planck gave us and then we get this number h. It's called Planck's constant and it's given by 6.66 times 10 to the -34 joules seconds. So that when I multiply by a frequency, which is one over seconds, then I'll get an energy, joules.

So, the way that we can understand Planck's constant is the ratio of photon energy that quantum that that discreet amount of energy that you can carry with a certain frequency f, to the frequency. So it's energy divided by frequency. And we got to get the same value for every single frequency. So this is the number that we get from blackbody radiation spectrum data. Alright. But that's not the only place that it shows up. It also shows up in the photoelectric effect. The photoelectric effect tells us that the maximum kinetic energy is given by some number times the frequency of light that you're shining on that metal surface minus a constant that depends only on the surface.

Now, according to Einstein, this hf is the photon energy. That's the way that it was explained to us and he won a Nobel Prize for that explanation. So h needs to have the same value when taken from photoelectric effect data and when taken from blackbody radiation spectrum data. And you know what, when we do the experiments, it works. It gives you exactly the same value. Alright. So let's go ahead and do some problems. These are fairly simple. We're just basically going to plug some numbers in a formula.

So how much energy is carried by a single photon with frequency 2 times 10 to the 12 hertz? Well, jeez. Energy equals hf 6.626 times 10 to the -34, 2 times 10 to the 12. Now as with everything when you got scientific notation what you want to do is the numbers first and then the tens. So, 2 times 6.626. Well, that's going to give us 13.2 what is it? 52 and then it will be times 10 to the what? Well, 12-34 is -22. What's the unit? Well, jeez. It's a energy. Everything was in SI units, so it's in SI units. So that's the answer, 13.252 times 10 to the -22 joules. Alright?

Let's do another one. How much energy is carried by a single photon and this time, I'm not giving you the frequency, giving you the wavelength. So we got to take the frequency in order to use e=hf. Well, e=hf but frequency and wavelength are related by frequency times wavelength, equals speed of light. So that means frequency is the speed of light divided by the wavelength and now it's just easy. So it's 6.626 10 to the -34 and then it's c is 3 times 10 to the 8 divided by, what was my wavelength? Well, it was 500 nanometers. But I'm supposed to work in SI units. So it's 500 nano is 10 to the -9. So we're going to say 5 times 10 to the -7. Alright. Numbers first. 6.626 times 3 over 5 and now e got the tens.