Question

The uncertainties in the velocities of two particles A and B are 0.05 and 0.02 $m.se{c}^{-1}$ respectively. The mass of B is five times to that of mass A.What is the ratio of uncertainties $\left[\frac{\Delta x_A}{\Delta x_B}\right]$ in their positions :

• A. 2
• B. 0.25
• C. 4
• D. 1

Answer 1

Answer: (A)

2

According to Heisenberg's uncertainty principle,

if $\Delta x$ is then uncertainty in the determination of the position and $\Delta p$ is the uncertainty in the determination of momentum of a very small moving particle then,

$\Delta x\Delta p=\frac{h}{4\pi }$

where h is Planck's constant the equation can also be expressed as,

$\Delta x\Delta v=\frac{h}{4\pi m}$ , because $\Delta p=m\Delta v$

As per the given condition,

$m_B=5m_A$, $\Delta v_A=0.05m(sec{)}^{-1}$, $\Delta v_B=0.02m(sec{)}^{-1}$

Therefore, $\frac{\Delta x_A}{\Delta x_B}=\frac{\Delta v_B{m}_B}{\Delta v_A{m}_A}$

Substituting the values,

$\frac{\Delta x_A}{\Delta x_B}=2$