Question

14. A table tennis ball has a mass of 10gm
and speed 15m/s. If the speed can
be measured within the accuracy of
2%.Calculate the uncertainty of the position.​

Answer 1

Answer :-

Uncertainty in position = 1.758 × 10⁻³⁴

Explanation :-

First find the uncertainty in speed.

For finding the Uncertainty in speed:

Uncertainty in speed = Given speed × Percentage

⇒ Uncertainty in speed = 15 × 2%

⇒ Uncertainty in speed = 15 × 2/100

⇒ Uncertainty in speed = 0.3 m/s

According to Heisenberg's Uncertainty Principle,

$\maltese \: \: \boxed{\pink{ \sf{ \Delta x \: . \: \Delta v = \dfrac{h}{4 \pi m} }}}$

where:

• ∆x is the uncertainty in position
• ∆v is the uncertainty in speed = 0.3 m/s
• h is Planck's constant = 6.626 × 10⁻³⁴
• π = 3.14

Substitute the given values in the equation.

$\implies \sf{\Delta x(0.3) = \dfrac{6.626 \times {10}^{ - 34} }{4 \times 3.14} }$

Dividing by 0.3 on both sides,

$\dashrightarrow \: \: \sf{ \Delta x = \dfrac{6.626 \times {10}^{-34} }{4 \times 3.14 \times 0.3} }$

$\dashrightarrow \: \: \sf{ \Delta x = \dfrac{6.626 \times {10}^{-34} }{3.768} }$

$\dashrightarrow \: \: \sf{ \Delta x = 1.758 \times {10}^{ - 34} }$

$\therefore \boxed{ \underline{ \red{\bf{\Delta x = 1.758 \times {10}^{ - 34} }}}}$

Answer 2

Answer:

Answer :-

Uncertainty in position = 1.758 × 10⁻³⁴

\begin{gathered}\\\end{gathered}

Explanation :-

First find the uncertainty in speed.

\begin{gathered}\\\end{gathered}

For finding the Uncertainty in speed:

Uncertainty in speed = Given speed × Percentage

⇒ Uncertainty in speed = 15 × 2%

⇒ Uncertainty in speed = 15 × 2/100

⇒ Uncertainty in speed = 0.3 m/s

\begin{gathered}\\\end{gathered}

According to Heisenberg's Uncertainty Principle,

\begin{gathered} \maltese \: \: \boxed{\pink{ \sf{ \Delta x \: . \: \Delta v = \dfrac{h}{4 \pi m} }}} \\ \\ \end{gathered}

✠

Δx.Δv=

4πm

h

where:

∆x is the uncertainty in position

∆v is the uncertainty in speed = 0.3 m/s

h is Planck's constant = 6.626 × 10⁻³⁴

π = 3.14

\begin{gathered}\\\end{gathered}

Substitute the given values in the equation.

\begin{gathered} \implies \sf{\Delta x(0.3) = \dfrac{6.626 \times {10}^{ - 34} }{4 \times 3.14} } \\ \\ \end{gathered}

⟹Δx(0.3)=

4×3.14

6.626×10

−34

Dividing by 0.3 on both sides,

\begin{gathered}\dashrightarrow \: \: \sf{ \Delta x = \dfrac{6.626 \times {10}^{-34} }{4 \times 3.14 \times 0.3} } \\ \\ \end{gathered}

⇢Δx=

4×3.14×0.3

6.626×10

−34

\begin{gathered} \dashrightarrow \: \: \sf{ \Delta x = \dfrac{6.626 \times {10}^{-34} }{3.768} } \\ \\ \end{gathered}

⇢Δx=

3.768

6.626×10

−34

\begin{gathered}\dashrightarrow \: \: \sf{ \Delta x = 1.758 \times {10}^{ - 34} } \\ \\ \end{gathered}

⇢Δx=1.758×10

−34

\begin{gathered} \therefore \boxed{ \underline{ \red{\bf{\Delta x = 1.758 \times {10}^{ - 34} }}}} \\ \\ \end{gathered}

∴

Δx=1.758×10

−34