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use the uncertainty principle to show that if an electron were confined inside and atomic nucleus, diameter of [tex]2 x 10^{-15}m[/tex], it would have to be moving relativistically i.e. more than 0.1c.

what i have done is the following:

[tex] \Delta x \Delta p = \frac{\hbar}{2}[/tex]

then i set [tex]\Delta x = 2 x 10^{-15}[/tex] and solved for [tex]\Delta p[/tex]

from this i dont know how to solve for the speed, i considered replacing [tex]\Delta p[/tex] with [tex]\gamma m\Delta v[/tex] but this doesnt seem to work with the gamma in there.

what is a better way to solve this?

thanks

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# Uncertainty principle and an electron

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