Question #122717
6. Assume that an electron is located somewhere within a region of atomic size. Estimate the minimum uncertainty in its momentum. By assuming that this uncertainty is comparable with its average momentum, estimate the average kinetic energy of the electron.
1
Expert's answer
2020-06-18T10:59:17-0400

According to the Heisenberg's uncertainty principle, the minimum uncertainty in momentum will be:


Δp=2Δx\Delta p = \dfrac{\hbar}{2\Delta x}

where =1.051034Js\hbar = 1.05\cdot 10^{-34}J\cdot s is the reduced Planck constant and Δx=1.061010m\Delta x = 1.06\cdot 10^{-10}m is the atom diameter (uncertainty of the coordinate). Thus:


Δp=1.051034Js21.061010m=51025kgm/s\Delta p = \dfrac{1.05\cdot 10^{-34}J\cdot s}{2\cdot 1.06\cdot 10^{-10}m} = 5\cdot 10^{-25} kg\cdot m/s

The average kinetic energy of the electron will be:


K=Δp22meK = \dfrac{\Delta p^2}{2m_e}

where me=9.111031kgm_e = 9.11\cdot 10^{-31}kg is the mass of electon.


K=(51025kgm/s)229.111031kg=1.371019JK = \dfrac{(5^\cdot 10^{-25} kg\cdot m/s)^2}{2\cdot 9.11\cdot 10^{-31}kg} = 1.37\cdot 10^{19}J


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS