Question

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

• A. $1\times {10}^{11}$ cm $s^{-1}$
• B. $1\times {10}^9$ cm $s^{-1}$
• C. $1\times {10}^6$ cm $s^{-1}$
• D. $1\times {10}^5$ cm $s^{-1}$

Answer 1

Answer: (B)

$1\times {10}^9$ cm $s^{-1}$

As per the Heisenberg's uncertainity principle equation,

momemtum is given by,

$\Delta p=m\Delta v$

Therefore, $\Delta v=\frac{1\times {10}^{-18}gcm{s}^{-1}}{9\times {10}^{-28}g}$

$\Delta v=0.92\times {10}^{10}cm/s\approx {10}^{9}cm/s$