Question

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?

Answer 1

"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,

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

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

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

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

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

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

Answer 2

Explanation:

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 }Δx.Δp≥

4π

h

\Delta x\quad =\quad Uncertainty\quad of\quad positionΔx=Uncertaintyofposition

\Delta p\quad =\quad Uncertainty\quad of\quad momentumΔp=Uncertaintyofmomentum

From the given,

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

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

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

100

4

×90=3.6

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

4πmΔv

h

=\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 }=

4×3.14×10×10

−3

×3.6

6.626×10

−34

\Delta x\quad =\quad 1.46\quad \times \quad { 10 }^{ -33 }\quad mΔx=1.46×10

−33

m "