At what speed in meters per second must a 145 g baseball be traveling to have a de Broglie wavelength of 0.500 nm?

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Everyone, we're told that a 12.5 g bullet is fired from a rifle, Calculate the speed the bullet needs in order to have a de Broglie wavelength of 3.5 nm. Now, to answer this question, we are going to have to use a formula of wavelength equals our plank's constant divided by our mass times velocity. So first let's go ahead and take our wavelength of 3.5 nanometers and convert this into meters. We know that we have 10 to the nine nanometers per one m. When we calculate this out, we end up with a wavelength of 3.5 times 10 to the -9 m. Now looking at our mass, we want to convert our 12.5 g into kg. Using our dimensional analysis. Again, we know that per one kg we have 10 to the 3rd g. So when we calculate this out, we end up with a mass of 1.25 times 10 to the -2 kg. Now, let's go ahead and calculate our velocity. We can rearrange our equation at the top and when we multiply velocity on both sides and divide our wavelength on both sides, we end up with an equation of velocity equals our plank's constant, divided by our mass times our wavelength. So, plugging in these values, we have our planks constant which is 6.626 times 10 to the negative 34 kg times meters squared over seconds. We will then divide this by our wavelength, which we calculated to be 3.5 times 10 to the -9 m. And we will also divide our mass, which we calculated to be 1.25 times 10 to the -2 kg. Now, when we calculate this out and cancel out all of our units, We end up with a velocity of 1.5 times 10 to the negative 23rd m/s, which is going to be our final answer. Now, I hope that made sense and let us know if you have any questions.

At what speed in meters per second must a 145 g baseball be traveling to have a de Broglie wavelength of 0.500 nm?

Verified Solution

Key Concepts

de Broglie Wavelength

Momentum

Unit Conversion