Question

The uncertainty in the location of circulating electron is equal to its de-Broglie wavelength. The minimum percent error in its measurement of velocity under this circumstance will be approximately:

• A. 8
• B. 9
• C. 7
• D. 6

Answer 1

The correct option is A 8

$△x\cdot △p=\frac{h}{4\pi }\Rightarrow △x(m\cdot △\nu )=\frac{h}{4\pi };△x=\lambda =\frac{h}{m\nu }$

$\therefore \frac{h}{m\nu }\cdot m△v=\frac{h}{4\pi }\Rightarrow \frac{△\nu }{\nu }=\frac{1}{4\pi }$

$\therefore \frac{△\nu }{\nu }$%$=\frac{100}{4\pi }\simeq 8$%