Calculate the de Broglie wavelength of a 143-g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?

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Welcome back everyone to another video, calculate the D poi wavelength of a 155 g bowl traveling at 82 MPH. Why is the wave nature of matter not important for this bowl? And we're given for answer choices. ABC and D, they essentially have a possible answer for each choice and a possible explanation. So what we're going to do is solve this problem using the deploy wavelength formula. Now what is the formula? Well, essentially we have to remember that lambda or the wavelength that we're interested in is equal to H which is planks constant divided by the momentum MV mass multiplied by velocity. What we're going to do in this problem is just calculate the result based on first of all blanks constant 6.626 multiplied by 10, the power of negative 34th J multiplied by second. So that's our planks constant. What about mass? Well, essentially we have 155 g. We want to use si units. So we're going to convert that into kilograms. We know that 1 kg is equivalent to 1000 g. Now, we need to use our velocity. We're given 82 MPH. And of course, let's recall that we are supposed to use meters per second. So here we are going to have a lot of conversions. First of all, we want to convert miles into meters and let's recall that one mile is equivalent to 1609 m. So this is how we get meters and eventually let's convert hours to seconds. One hour is equivalent to 3600 seconds. We have our set up, we are ready to get our final answer for this problem. So now if we perform the calculations, we end up with 1.2 multiplied by 10, the power of negative 34th of a meter. Now let's carefully look at this exponent. Notice that it's so extremely small, it's in the magnitude of sensitive power of negative 34. So we can say that this wavelength is timing, that's what we can say. And because it's so small, it will essentially not affect the trajectory of the ball, right? Let's remember that wavelengths that are important for us start at at least one or 10 nanometers. And this is much, much smaller to affect the trajectory of a ball. This is usually common or objects that we encounter in real life that have big dimensions, significantly large mass and travel at significantly large speeds. So what we can say is that based on the answer choices, the correct answer to this problem would be option A which essentially states that the correct answer is 1.2 multiplied by 10 to the power of negative 34th of a meter. And the value of wavelength is so small that it will not affect the trajectory of the ball. That would be it for today. And thank you for watching.

Calculate the de Broglie wavelength of a 143-g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?

Verified Solution

Key Concepts

de Broglie Wavelength

Momentum

Wave-Particle Duality