An electron is trapped within a sphere that has a diameter of5.0 x 10 -15 meters

Question

An electron is trapped within a sphere that has a diameter of5.0 x 10-15 meters (about the size of a nucleus of asilicon atom).    a) What is the minimum uncertainty in theelectron's momentum?    b) If the electron's de Broglie wavelengthis the same as the diameter of the sphere, whatwould be its momentum? An electron is trapped within a sphere that has a diameter of5.0 x 10-15 meters (about the size of a nucleus of asilicon atom).    a) What is the minimum uncertainty in theelectron's momentum?    b) If the electron's de Broglie wavelengthis the same as the diameter of the sphere, whatwould be its momentum?

Explanation / Answer

electron is trapped at the position   x =5*10-15 m minimum uncertainty in electron 's momentum               P    = h / 4 x                        = 6.63*10-34 J . s   / 4 (5*10-15 m )                        = 0.42 *10-19   kg . m/s debriglie wavelength of electron is   =5*10-15 m       momentum of electron                         P = h /                             = 6.63*10-34 J . s   / ( 5*10-15 m)                              =1.326*10-19   kg . m/s

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