Question

The minimum values of uncertainties involved in the determination of both the position and velocity of a particle are respectively $1 \times 10^{-10}m$ and $1 \times 10^{-10} ms^{-1}$. 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

Answer: (A)

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

Uncertainty in velocity

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

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

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

$=\frac{6.62 .6 \times 10^{-31}}{4 \times 3.14 \times 10^{-10} \times 10^{-10}}$

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