Question

An electron is accelerated to one-tenth the velocity of light. Suppose its velocity can be measured with a precision of 1%, what must be the uncertainty in position?

• A. $2.13\times {10}^{-10}$
• B. $1.93\times {10}^{-10}$
• C. $3.85\times {10}^{-10}$
• D. $1.52\times {10}^{-10}$

Answer 1

Answer: (B)

$1.93\times {10}^{-10}$

The velocity of electron is one tenth the velocity of light. It is $0.1\times 3\times {10}^{8}m/s=3\times {10}^{7}m/s$
The precision is 1%. Hence, the uncertainity in velocity is $\Delta V=0.01\times 3\times {10}^7=3\times {10}^{5}m/s$
The uncertainity in position is $\Delta x=\frac{h}{4\pi m\Delta V}=\frac{6.626\times {10}^{-34}}{4\times 3.1416\times 9.1\times {10}^{-31}\times 3\times {10}^5}=1.93\times {10}^{-10}m$