Question

Calculating the uncertainty in the position of a dust particle with mass equal to 1 mg if uncertainty in its velocity is 5.5 × 10? 64 m/s.

Answer 1

$\boxed{ \huge{ \mathfrak{ \fcolorbox{red}{yellow}{\purple{Answer}}}}} \\ \\ \star \: \red{\mathfrak{Given}} \\ \\ \implies \rm \: uncercertainty \: in \: velocity \: \triangle{v} = 5.5 \times {10}^{64} \: \frac{ m}{s} \\ \\ \implies \rm \: mass \: of \: particle \: m = 1mg = {10}^{ - 6} kg \\ \\ \star \: \red{ \mathfrak{To \: Find}} \\ \\ \implies \rm \: uncertainty \: in \: position \: \triangle{x} \\ \\ \star \: \red{ \mathfrak{Formula}} \\ \\ \implies \: \boxed{ \rm{ \pink{ \triangle{x} \times m( \triangle{v}) = \frac{h}{4\pi} = 5 .27\times {10}^{ - 35} }}} \\ \\ \star \: \red{ \mathfrak{Calculation}} \\ \\ \implies \rm \: \triangle{x} = \frac{5.27 \times {10}^{ - 35} }{m \times \triangle{v}} \\ \\ \implies \rm \: \triangle{x} = \frac{5.27 \times {10}^{ - 35} }{ {10}^{ - 6} \times5.5 \times {10}^{64} } = 0.1 \times {10}^{ - 93} \: m \\ \\ \implies \: \boxed{ \mathfrak{ \orange{ \triangle{ \rm{x}} = 1 \times {10}^{ - 94} \: m}}}$