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XJellieBX
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Homework Statement
Using the uncertainty relation for momentum and position, show that the quantum-mechanical uncertainty in the position of a particle at temperture T is
[tex]\Delta x[/tex]~[tex]\sqrt{\frac{h^{2}}{4mkT}}[/tex]
where T is the temperature and k is the Boltzmann's constant.
Homework Equations
[tex]\Delta p\Delta x\geq h/2[/tex], h being Planck's constant
K.E.=0.5 mv2=0.5 kT
The Attempt at a Solution
I isolated [tex]\Delta x[/tex] and subbed [tex]\Delta p[/tex]=mv=kT/v.
So, [tex]\Delta x[/tex]~h/2[tex]\Delta p[/tex] ~ h/2mv ~ hv/2kT.
I've tried subing in a whole bunch of stuff for v but I can't seem to get the equation. Any insight?