The measurement of the electron position is associated with an uncertainty in momentum which is equal to $1

Question

The measurement of the electron position is associated with an uncertainty in momentum which is equal to $1 	imes 10^{-18} 	ext{ g cm s}^{-1}$. The uncertainty in velocity of the electron will be: (mass of an electron is $9 	imes 10^{-28} 	ext{ g}$)

Accepted Answer

The uncertainty in momentum ($\Delta p$) is related to the uncertainty in velocity ($\Delta v$) and mass ($m$) by the definition of momentum: $\Delta p = m \cdot \Delta v$.

1.  **Identify Given Values:**
    *   Uncertainty in momentum ($\Delta p$) = $1 	imes 10^{-18} 	ext{ g cm s}^{-1}$
    *   Mass of electron ($m$) = $9 	imes 10^{-28} 	ext{ g}$

2.  **Calculation:**
    Rearranging the formula to solve for $\Delta v$:
    $$ \Delta v = \frac{\Delta p}{m} $$
    $$ \Delta v = \frac{1 	imes 10^{-18}}{9 	imes 10^{-28}} $$
    $$ \Delta v = \frac{1}{9} 	imes 10^{10} 	ext{ cm s}^{-1} $$
    $$ \Delta v \approx 0.111 	imes 10^{10} 	ext{ cm s}^{-1} $$
    $$ \Delta v \approx 1.11 	imes 10^9 	ext{ cm s}^{-1} $$

Rounding to the nearest integer coefficient as per the options, the value is $1 	imes 10^9 	ext{ cm s}^{-1}$.

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