What is the de Broglie wavelength in meters of a baseball weighin...

Question

What is the de Broglie wavelength in meters of a baseball weighing 145 g and traveling at 156km/h? Why do we not observe this wavelength?

Accepted Answer

Hey everyone, we're asked to calculate the day broccoli wavelength for a 45. g golf ball moving at 340 kilometers per hour. Is this wavelength observable as we've learned, Our wavelength is equal to our plank's constant, divided by our mass, times our velocity. So first let's go ahead and determine our mass. We can go ahead and take our 45.9 g golf ball and we can convert this into kilograms. So we know that we have 10 to the 3rd g per one kg And this will get us to a mass of 0.0459 kg. Now, to calculate our velocity, We can take our 340 km per one hour and we want to convert this into meters per second. So we know that per one km we have 10 to the 3rd m And per one hour we have 3600 seconds. So when we calculate this out and cancel out all of our units, we end up with a velocity of 94.4444 m/s. Now, let's go ahead and calculate our wavelength. We can go ahead and plug in our values. So we have 6.626 times 10 to the negative 34 kg times meters squared per seconds. And this is our planks constant. We can then go ahead and divide this by our mass which is 0. kg. And also our velocity, which we calculated to be 94. m per second. And when we calculate this out and cancel out all of our units, We end up with a wavelength of 1.53 times 10 to the -34 m which is going to be our final answer. Now to answer the last question, which was whether this wavelength is observable, the answer is going to be that this wavelength is too small to be observed, and this is also going to be our final answer. Now, I hope that made sense and let us know if you have any questions.

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