What Happens to the de Broglie Wavelength as Mass Approaches Infinity?

AI Thread Summary
As mass approaches infinity in the de Broglie wavelength formula, the wavelength approaches zero, suggesting that massive particles behave more like point particles. This implies that larger mass particles do not exhibit significant wave-like properties, allowing for the application of classical Newtonian physics. The de Broglie wavelength equation indicates that all particles theoretically exist as waves, but practical observations show that high-mass objects, like a cricket ball, do not demonstrate these wave characteristics. Thus, the discussion highlights the transition from quantum to classical behavior as mass increases. Ultimately, the relationship between mass and wave-like properties is crucial in understanding the limits of quantum mechanics in classical physics.
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If, in the expression for the de Broglie wavelength, we let m -> infinity, do we get the classical result for matter?

de Broglie wavelength = h/mv

so as m goes to infinity the de Broglie wavelength goes to 0. So does this mean that particles with larger mass don't display wavelike properties and therefore can be treated as a point particle which means we can apply classical Newtonian physics?
 
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The de Broglie wavelength assumes that ALL particles exist as a wave with wavelength h/mv
 
Yeah I understand that but if their wavelength is small enough they don't display (a cricket ball doesn't display wave like properties) wave like properties?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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