In the ground state of hydrogen, the uncertainty in theposition of the electron

Question

In the ground state of hydrogen, the uncertainty in theposition of the electron is roughly 0.09 nm. The mass of an electron is 9.10939e-31 kg and the Plank'sconstant is 6.62607e-34 j*s. If the speed of the electron is on the order of theuncertainty in the speed, how fast is the electron moving? Answer in units of m/s. In the ground state of hydrogen, the uncertainty in theposition of the electron is roughly 0.09 nm. The mass of an electron is 9.10939e-31 kg and the Plank'sconstant is 6.62607e-34 j*s. If the speed of the electron is on the order of theuncertainty in the speed, how fast is the electron moving? Answer in units of m/s.

Explanation / Answer

The mass of an electron is m = 9.10939e-31kg the Plank's constant h = 6.62607e-34 j*s. from the relation d x . m dv = ( h / 2 ) from this the uncertainty in the speed is d v = ( h /2) / m dx                                                                  = 1.286 * 10 ^ 6 m / s

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