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What is the de Broglie wavelength (in $\mathrm{nm}$ ) associated with a $2.5-\mathrm{g}$ Ping-Pong ball traveling $35 \mathrm{mph} ?$

To use this formula we need to convert the data provided to the corresponding formula units:Grams to kilograms:$2.5 g \cdot \frac{k g}{1000 g}=0.0025 k g$Miles/h to $m / s$$35 \frac{\text {miles}}{h} \cdot \frac{1.61 \mathrm{km}}{1 \mathrm{mile}} \cdot \frac{1000 \mathrm{m}}{1 \mathrm{km}} \cdot \frac{h}{3600 \mathrm{s}} \approx 15.65 \frac{\mathrm{m}}{\mathrm{s}}$Now we replace variables by data in equation (1) and solve$\lambda=\frac{6.63 \cdot 10^{-34} \cdot \frac{m^{2} \cdot k g}{s}}{0.0025 k g \cdot 15.65 \frac{m}{s}} \approx 1.69 \cdot 10^{-32} m=1.69 \cdot 10^{-23} \mathrm{nm}$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Carleton College

University of Kentucky

Brown University

Lectures

04:49

In chemistry and physics, electronic structure is the way the electrons of an atom are arranged in relationship to the nucleus. It is determined by the subshells the electrons are bound to, which are in turn determined by the principal quantum number ("n") and azimuthal quantum number ("l"). The electrons within an atom are attracted to the protons in the nucleus of that atom. The number of electrons bound to the nucleus is equal to the number of protons in the nucleus, which is called the atomic number ("Z"). The electrons are attracted to the nucleus by this mutual attraction and are bound to the nucleus. The electrons within an atom are attracted to each other and this attraction determines the electron configuration. The electron configuration is described by the term symbol, which is the letter used to identify each subshell.

16:45

In physics, the wave–particle duality is the concept that every object or process, no matter how large or how small, behaves as both a wave and a particle. The wave–particle duality is one of the central concepts in quantum mechanics.

10:17

What is the de Broglie wav…

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Calculate the de Broglie w…

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okay. This problem were asked to find the Burghley wavelength of a ping Pong ball. So we know that the Jew Burghley wavelength is shown as wavelength equals. Plank's constant, divided by mass times philosophy he's made. So we know that we need to find mass and velocity, but we need to change. We needed Teoh change. What terms there in velocity is given in MPH, a massive given in grams. So we need master P a kilograms and we need velocity to be in litres per second. So you go ahead, do some juicing conversions. So mass says 2.5 grams. Go ahead and convert that two kilograms by dividing it because we know there's 1000 grams in a kilogram. So we go ahead and divide that by 1000 so that we get zero point zero to your 0.25 kilograms. So that one was easy enough. So now we need to convert from MPH two meters per second. So that is going So let's go ahead and say 35 MPH and we know that you know that there is 1.61 kilometers in every mile. All rights. Now we're in kilometers. And now let's go ahead and convert from kilometers two meters. So in one kilometer there are 1000 meters. She now we're in meters per hour if we were to stop here. But we know that there are 3600 seconds for our. So when we do that conversion, this will give us speed of 15.65 meters per second. So now we can go ahead, plug the's all in. So we get the two broke the wavelength. It's evil to 6.63 times Senator the negative 34th. We know that that is the plank's constant. I mean, that is in units off Jules per second, and it's really divided by mass in kilograms, which you just found up here. So is your point 00 25 kilograms times 15 0.65 years. Her second, so second's gonna cancel out. And jewels is actually is also considered mere squared times, kilogram per second. So, Jules, this meters in this meter or this kilograms is going to cancel out. We're gonna be left with terms of meters. Wavelength is equal to 1.69 times 10 to the negative 32 meters. So this is incredibly small wavelength, which makes sense, because as the larger the object is, the smaller its wavelength. Now, if we want to convert this into Nana meters, we would multiply by 10 to the ninth. Because we know that for every one meter, there are 10 to the ninth Nana meters. So that would give us 1.69 times 10 to the negative 23rd man, um, years again, very, very small number. That would be your answer. Thank you very much.

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