Mass of an Object in the DeBroglie Equation


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Samantha Pedersen 2K
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Mass of an Object in the DeBroglie Equation

Postby Samantha Pedersen 2K » Mon Oct 19, 2020 12:19 pm

In lecture today, Dr. Lavelle mentioned that the mass of the object dominates over the velocity in determining what the wavelength of the object is. Why is it the case that the mass plays a larger role than the velocity in determining the wavelength of the object? Are there any cases where the velocity plays a larger role in determining the wavelength of the object?

EnricoArambulo3H
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Re: Mass of an Object in the DeBroglie Equation

Postby EnricoArambulo3H » Mon Oct 19, 2020 12:25 pm

If you consider the mass of an electron (9.11*10^-31 kg), and compare it to the exponent of Planck's constant (10^-34), you would see that it would cause the resulting exponent to be around 10^-3. In contrast, take a sample mass of 1.5 kg. If you divide the Planck's constant by the mass, you will get a resulting exponent of around (10^-34). Since you have these exponents without factoring in velocity (max velocity is speed of light), the resulting wavelength will be even smaller. I hope this wasn't too confusing!

Annika Tamaki 1E
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Re: Mass of an Object in the DeBroglie Equation

Postby Annika Tamaki 1E » Mon Oct 19, 2020 12:33 pm

All masses have wavelike property, but only small objects can be observed to have these wavelike properties. This is because momentum=mass*velocity. If an object has a large mass, it will have a large momentum as well. Since wavelength=h/momentum, mass and wavelength are inversely proportional. So if an object has a large mass and a large momentum, it will result in an unmeasurable wavelength. Since any object that is moving, or that has a velocity, will result in a wavelength, it is up to the mass to determine whether we can observe that wavelength or not. Hope this helps!

Benjamin Chen 1H
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Re: Mass of an Object in the DeBroglie Equation

Postby Benjamin Chen 1H » Mon Oct 19, 2020 12:34 pm

Mass plays a larger role because velocity is capped at the speed of light, which is only around 10^8 and mass is more capable of having a 10^(negative number).

Since Planck's Constant is around 10^-34 and the cut off is around 10^-15, mass can have a really small value to create an observable wavelength.

Maybe it makes more sense if you compare two objects of different mass but going at the same velocity to two objects of the same mass going at different velocities. In the different mass example, the difference in mass can be 10, 100, or even 1 trillion (or more) times in ratio creating a large impact on the wavelength difference. While in the same mass example, the difference in velocity is much more limited in it's range of speeds creating a smaller impact on the wavelength difference.

Sorry if this didn't make it concrete because I started to question why, also, halfway in my explanation...


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