Calculate the de Broglie wavelength of a 143-g baseball traveling...

Question

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?

Accepted Answer

Hey everyone in this example, we need to find the D, Broccoli wavelength associated with our bowling ball that is rolling at a speed of 16 mph and we also need to explain in part to why the wave nature of matter is insignificant for our bowling ball. So what we want to recall is our formula for wavelength and we want to recall that this is a symbol for wavelength and that's equal to plank's constant in the numerator, divided by our mass of our object, multiplied by its velocity. Now we want to recall that our units for velocity Um are given here in the question as 16 mph. But we want to go ahead and recall that our velocity should always be in meters per second for this formula. So we're going to have to make a conversion there So we can begin that conversion by taking our velocity given to us as 16 mph and we're going to want to cancel out that miles term first. So we're going to recall that in one mile, We have 1.609 km And now we can go ahead and get rid of that miles unit leaving us with kilometers to cancel out next. And so our next conversion factor to recall is that for one km We have 10 to the third power m. So this allows us to then cancel out kilometers and next we'll focus on getting rid of that, our term in our denominator here. And so we want to go ahead and multiply by the conversion factor where we have in one hour seconds. So this allows us to get rid of hours leaving us with meters per second as our final units for velocity. And this gives us a velocity value equal to 7.1511 m per second. So now we can go ahead and focus on plugging and everything into our formula. So what we would have is that our wavelength is equal to in our numerator, we should have plank's constant. So recall that. That's 6.626 Times 10 to the negative 34th power jewels, times seconds. And then in our denominator we have our mass of our bowling ball which is given to us in the problem as 5.44 kg. So we plugged it in 5.44 Kg for a bowling ball. And then this is multiplied by our velocity, which we just converted to the proper units as 7.1511 m/s. And so now we're just going to want to simplify our numerator part where we have planks constant by recalling that our jewel unit is also interpreted as kilograms times meters squared divided by second squared. So we're going to substitute this in place of our jewels. And so that should read as our wavelength being set equal to Planck's constant and numerator 6.6 26 times 10 to the negative 34th power. And then we're substituting for jules, kilograms times meters squared divided by second squared. And then this is still being multiplied by seconds as it was in the numerator over here. So now that we have simplified the numerator, we're going to go ahead and Also simplify our denominator by multiplying these two terms in our denominator are mass and our velocity. And so that's going to give us a value and our denominator equal to 38.902 kilograms times meters divided by seconds. So we can go ahead and calculate our final result for wavelength. But before we type that in our calculators, we want to go ahead and cancel out our units. So looking at our units, we can get rid of the kilogram units. We can get rid of our seconds in the numerator. Up here with the second here, we can get rid of our meter term, leaving us with meters to the first power in the numerator. And then we can also get rid of our last seconds term here, Which leaves us with just meters as our only unit left. And so when we calculate this whole quantity in our calculators, we're going to get a value equal to 1.70 times 10 to the negative 35th power. And then again we're left with meters to the first power. So that's just meters. So based on this very low number for our wavelength, we're going to basically be able to answer part Two of this question because this is our answer for Part one, which is our very low value for wavelength. So considering how low this magnitude is for our wavelength, we can say that due to the small magnitude, we can say our bowling ball momentum will be unaffected. And so that answers as to why the wave nature of matter is insignificant for our bowling ball. And again, because our magnitude of our wavelength is so small based on our calculation here for the wavelength. So everything boxed in blue is our final answers for both parts of this question. I hope that everything we reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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