When studying quantum mechanics, the de Broglie wavelength is a key idea. De Broglie wavelength is the wavelength () that is connected to an item in relation to its momentum and mass.
Typically, a particle's force is inversely proportional to its de Broglie wavelength.
Assuming that the smallest measurable wavelength in an experiment is 0.830 fm , what is the maximum mass of an object traveling at 171 m⋅s−1 for which the de Broglie wavelength is observable?
We know:
- The shortest wavelength that is detectable, λm = 0.330 fm
- the object's velocity, v = 157 m/s
According to the following equation, an object's de-Broglie wavelength solely depends on its momentum:
λ = h/p = h/m*v, where,
- h = 6.626 × 10^(−34) J⋅s
- p = mv is the object's momentum. It is based on the moving object's mass, m, and velocity, v.
By rearranging the above equation, the object's mass can be written as:
m = h/λv
The maximum mass and the minimum de Broglie wavelength of the item are inversely correlated because the two quantities are inversely proportional to one another. When we enter the values provided, we get:
m = {6.626×10^(−34) J⋅s} / {0.330 fm × 157 m/s}
≈ 1.28×10^(−20) kg
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