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If the uncertainties in the measuremen...

If the uncertainties in the measurement of position and momentum of an electron are equal calculate the uncertainty in measuring the velocity

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According to de Broglie equation `Delta x - Delta p = (h)/(4pi)`
Since `Delta x = Delta p` therefore `Delta x = Delta p sqrt((h)/(4pi)) = 0.729 xx 10^(-17)`
Also `Delta x = Delta v, (h)/(4pi m) xx sqrt((4pi)/(h))`
`= sqrt(4)/(4pi)) xx (1)/(m)`
`= (0.726 xx 10^(-17))/(9.1 xx 10^(-31)) = 7.98 xx 10^(12) m s^(-1)`
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Uncertainty in Measurement

Werner Heisenberg considered the limits of how precisely we can measure the properties of an electron or other microscopic particle. He determined that there is a fundamental limit to how closely we can measure both position and momentum. The more accurately we measure the momentum of a particle, the less accurately we can determine its position. The converse is also true. this is summed up in what we now call the Heisenberg uncertainty principal. The equation is Deltax.Delta(mv) ge (h)/(4pi) The uncertainty is the position or in the momentum of a macroscopic object like a baseball is too small to observe. However, the mass of microscopic object such as an electron is small enough for the uncertainty to be relatively large and significant. If the uncertainties in position and momentum are equal, the uncertainty in the velocity is:

Werner Heisenberg considered the limits of how precisely we can measure the properties of an electron or other microscopic particle. He determined that there is a fundamental limit to how closely we can measure both position and momentum. The more accurately we measure the momentum of a particle, the less accurately we can determine its position. The converse also true. This is summed up in what we now call the Heisenberg uncertainty principle. The equation si deltax.delta (mv)ge(h)/(4pi) The uncertainty in the position or in the momentum of a marcroscopic object like a baseball is too small to observe. However, the mass of microscopic object such as an electon is small enough for the uncertainty to be relatively large and significant. If the uncertainties in position and momentum are equal, the uncertainty in the velocity is :

If uncertainty in position and momentum of a particle of mass 'm' are equal then minimum uncertainty in velocity will be :-

A german physicist gae a principle about the uncertainties in simultaneous measurement of position and momentum of small particles. According to that physicist. It is impossible to measure simultaneously the position and momentum of small particle with absolute accuracy or certainty. if an attempt is made to measure any one of these two quantities with higher accuracy, the other becomes less accurate. The produce of the uncertainty in position (Deltax) and uncertainty momentum (Delta p) is always constant and is equal to or greater than h//4pi , where h is Planck's constant i.e. (Deltax ) (Deltap) ge (h)/(4pi) If uncertainty in momentum is twice the uncertainty in position of an electron then uncertainty in velocity is: [bar(h)=(h)/(2pi)]

CENGAGE CHEMISTRY-ATOMIC STRUCTURE-Concept Applicationexercise(4.3)
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  16. How many spectrical nodal syrface are there in a. a 3s orbital b. a...

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