Question

A golf ball has a mass of 40 kg, and a speed of 45 m/s. If the speed can be measured within the accuracy of 2%. Calculate the uncertainty in the position.

Answer 1

$\huge\bf{\color{indigo}GIVEN}$

• Mass of a golf ball is 40g.

• Speed of that golf ball has 45 m/s.

✈︎ The speed can be measured within the accuracy of 2%.

$\huge\bf\blue{TO\:FIND}$

• The uncertainty in the position.

$\huge\bf\orange{SOLUTION}$

☘️ We know the Heisenberg uncertainty principle,

$\red\bigstar\:\bf\purple{\triangle{x}\:=\:\dfrac{h}{4\pi{m}\triangle{v}}\:}$

$\bf\pink{Where,}$

• ∆x = Uncertainty in the position.

• h = Planks Constant.

• m = mass of particle velocity.

• ∆v = Uncertainty in the velocity.

$\bf{\color{lime}We\:have,}$

• h = $\bf\gray{6.626\times{10^{-34}}\:J.s}$

• π = $\bf\gray{3.14}$

• m = $\bf\gray{40\:g\:=\:0.04\:kg}$

• ∆v = 2% of v $\sf{=\:\dfrac{2}{100}\times{45}\:=\:\gray{0.9\:m.s^{-1}}}$

$\hookrightarrow\:\bf{\triangle{x}\:=\:\dfrac{6.626\times{10^{-34}}}{4\times{3.14}\times{0.04}\times{0.9}}\:}$

$\hookrightarrow\:\bf{\triangle{x}\:=\:\dfrac{6.626\times{10^{-34}}}{0.45216}\:}$

$\hookrightarrow\:\bf\green{\triangle{x}\:=\:14.6541\times{10^{-34}}\:m}$

$\huge\red\therefore$ The uncertainty in the position is $\bf{\triangle{x}\:,i.e.\:\blue{14.6541\times{10^{-34}}\:m}}$.