Question

The minimum values of uncertainties involved in the determination of both the position and velocity of a particle respectively are $1\times {10}^{-10}m$ and $1\times {10}^{-10}m{s}^{-1}$. Then, the mass (in kg) of the particle is :

• A. $5.270\times {10}^{-15}$
• B. $5.270\times {10}^{20}$
• C. $5.270\times {10}^{-16}$
• D. $5.270\times {10}^{-10}$
• E. $5.270\times {10}^{-14}$

Answer 1

The correct option is A $5.270\times {10}^{-15}$

Given uncertainty in position $=1\times {10}^{-10}m$

Uncertainty in velocity

$=1\times {10}^{-10}m/s$

From equation $m\times \Delta v\times \Delta x=\frac{h}{4\pi }$

So, $m=\frac{h}{4\pi \times \Delta x\times \Delta v}$

$=\frac{6.626\times {10}^{-34}}{4\times 3.14\times {10}^{-10}\times {10}^{-10}}$

Mass (m) $=5.27\times {10}^{-15}kg$

Hence, the correct option is $\text{A}$