Calculate the minimum values of momentum and velocity uncertainties, delta p_x a

Question

Calculate the minimum values of momentum and velocity uncertainties, delta p_x and delta ?_? = delta_px, for a bound electron in an atom, where delta x = 0.053 nm. The electron mass is 9.1 times 10^-31 kg, and h = 6.626 times 10^-34 J s. Now we consider that delta p_x is really the root-mean-square deviation in p_x: delta p_x = ((Delta p_x)^2)^1/2 with Delta p_x = px - (px) Here, the pointed brackets (...) represent quantum-mechanical averaging ("expectation value"). Treat this like a statistical average in the following: Calculate the minimum values of momentum and velocity uncertainties, delta p_x and delta ?_? = delta_px, for a bound electron in an atom, where deltax = 0.053 nm. The electron mass is 9.1 times 10^-31 kg, and h = 6.626 times 10^-34 J s. Now we consider that delta p_x is really the root-mean-square deviation in p_x: delta p_x = ((Delta p_x)^2)^1/2 with Delta p_x = px - (px) Here, the pointed brackets (...) represent quantum-mechanical averaging ("expectation value"). Treat this like a statistical average in the following:

Explanation / Answer

A) according to uncertainty relation px x = /2

px = h /(4pi x) = 6.626x1034 /(4x3.14x0.053x109)=9.9537×10-25

px = 9.9537×10-25

vx = px /m = 9.9537×10-25 / 9.1×10-31 =1.09×106

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