Question

calculate the uncertainty in the velocity of an electron if the uncertainty in its position is 1Å
or 100pm (10^-10m).​

Answer 1

QUESTION ⤵️

calculate the uncertainty in the velocity of an electron if the uncertainty in its position is 1Å or 100pm (10^-10m).

ANSWER ⤵️

HERE WE ARE GIVEN,

$ΔX = {10}^{ - 10} m$

$h = 6.6 \times {10}^{ - 34}{kg} \: {m}^{2} {s}^{ - 1}$

$m = 9.1 \times {10}^{ - 31} kg$

Applying uncertainty principle,

$ΔX.(mΔv) = \frac{h}{4\pi}$

i.e.,

$Δv = \frac{h}{4\pi \times m \times ΔX }$

$= \frac{ \:6.6 \times {10}^{ - 31}kg {m}^{2} {s}^{ - 1} \: }{4 \times \frac{22}{7} \times 9.1 \times {10}^{ - 31}kg \times {10}^{ - 10} m}$

$:\longrightarrow\pink{5.77 \times {10}^{5} m {s }^{ - 1} }$

$\purple{BE \: \: BRÃÎÑLY❥}$

$†HOPE \: IT \: HELPS†$