Question

The uncertainty in position and velocity of a particle are $10^{-10}\, m$ and $5.27 × 10^{-24}\, ms^{-1}$ respectively. Calculate the mass of the particle is $(h = 6.625 × 10^{-34}\, J-s) $

• A. $0.099\,kg$
• B. $0.99\,kg$
• C. $0.92\,kg$
• D. None

Answer 1

Answer: (A)

According to Heisenberg’s uncertainty principle,
$\Delta x.\,m\,\Delta v=\frac{h}{4\pi}$
or $m=\frac{h}{4\pi\,\Delta x.\,\Delta v}$
$=\frac{6.625\times10^{-34}\,Js}{4\times3.143\times10^{-10}\,m\times5.27\times10^{-24}\,ms^{-1}}$
$\because\left[J=Kgm^{2}s^{2}\right]$
$=0.099\,kg.$