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In the ground state ofhydrogen, the uncertainty in the position of the electron

ID: 1758045 • Letter: I

Question

In the ground state ofhydrogen, the uncertainty in the position of the electron isroughly 0.15nm. The mass of ane electron is 9.10939 × 1031 kg and thePlanck’s constant is 6.62607 × 1034 J· s. If thespeed of the electron is on the order of the uncertainty in thespeed, how fast is the electron moving? Answer in units ofm/s. I tried this method, but I think I'mdoing something wrong. Please check! Could the steps please beexplained, thanks. ( h/ 2 ) / [ m dx ]= 771,784 m / s In the ground state ofhydrogen, the uncertainty in the position of the electron isroughly 0.15nm. The mass of ane electron is 9.10939 × 1031 kg and thePlanck’s constant is 6.62607 × 1034 J· s. If thespeed of the electron is on the order of the uncertainty in thespeed, how fast is the electron moving? Answer in units ofm/s. I tried this method, but I think I'mdoing something wrong. Please check! Could the steps please beexplained, thanks. ( h/ 2 ) / [ m dx ]= 771,784 m / s I tried this method, but I think I'mdoing something wrong. Please check! Could the steps please beexplained, thanks. ( h/ 2 ) / [ m dx ]= 771,784 m / s

Explanation / Answer

From the uncertainity in position and momentum we have :                      x P   ˜   h /4                   x (mv) ˜   h /4                  (since momentum P = mass * velocity = m v)                   x m (v)˜   h /4         or            v      =   h /4 *(x * m )       Given :                                  x     =   0.15 nm  = 0.15   x 10-9 m                h      =   6.626 x 10-34    J-s               m      = 9.11 x 10-31   kg           v    =   (6.626 x 10-34    J-s ) /4*3.14*( 0.15   x 10-9 m *  9.11 x 10-31   kg )                        =  0.386057 x 106    m /s                        = 386,057 m/s Hope this helps u!               
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