Table tennis ball has a mass of 10 g

Asked by admin @ 20/08/2021 in Chemistry viewed by 293 People

Table-tennis ball has a mass 10 g and a speed of 90 m/s. If speed can be measured within an accuracy of 4% what will be the uncertainty in speed and position?

Answered by admin @ 20/08/2021

"Heisenberg Uncertainty principle:

It is fundamentally impossible to know precisely both the velocity and the position of a particle at the same time.

$\Delta x.\Delta p\quad \ge \quad \frac { h }{ 4\pi }$

$\Delta x\quad =\quad Uncertainty\quad of\quad position$

$\Delta p\quad =\quad Uncertainty\quad of\quad momentum$

From the given,

$Mass\quad of\quad ball\quad =\quad 4\quad g$

$Speed\quad =\quad 90\quad m/s$

$\Delta \upsilon \quad =\quad \frac { 4 }{ 100 } \quad \times \quad 90\quad =\quad 3.6$

$\Delta x\quad =\quad \frac { h }{ 4\pi m\Delta v }$

$=\quad \frac { 6.626\quad \times { \quad 10 }^{ -34 } }{ 4\quad \times \quad 3.14\quad \times \quad 10\quad \times \quad { 10 }^{ -3 }\quad \times \quad 3.6 }$

$\Delta x\quad =\quad 1.46\quad \times \quad { 10 }^{ -33 }\quad m$ "

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Table tennis ball has a mass of 10 g

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