Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

If uncertainties in the measurement of position and momentum are equal,calculate uncertainty in the measurement of velocity.

$\begin{array}{1 1}(a)\;7.98\times 10^{12}m/s&(b)\;6.98\times 10^{12}m/s\\(c)\;7.98\times 10^6m/s&(d)\;5.83\times 10^{12}m/s\end{array}$

Can you answer this question?

1 Answer

0 votes
Heisenberg's uncertainty principle
$\Delta x.\Delta p\geq \large\frac{h}{4\pi}$
$\Delta x=\Delta p$,hence
$\Delta x=\Delta p=\sqrt{\large\frac{h}{4\pi}}$
$\Rightarrow 0.726\times 10^{-17}$
Also $\Delta x.\Delta v\geq \large\frac{h}{4\pi m}$
Thus $\Delta v=\large\frac{\Large\frac{h}{4\pi m}}{\Delta x}$
$\Rightarrow \large\frac{4/4\pi m}{\sqrt{h/4\pi}}$
$\Rightarrow \sqrt{\large\frac{h}{4\pi}}\times \large\frac{1}{m}$
$\Rightarrow \large\frac{0.726\times 10^{-17}}{9.1\times 10^{-31}}$
$\Rightarrow 7.98\times 10^{12}m/s$
Hence (a) is the correct answer.
answered Jan 16, 2014 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App