Question

A molecule of roughly spherical shape has a mass of 6.10 × 10-25 kg and a diameter of 0.70 nm. The uncertainty in the measured position of the molecule is equal to the molecular diameter. What is the minimum uncertainty in the speed of this molecule? (h = 6.626 × 10-34 J · s)

Answer 1

Answer:

$\Delta v = 0.123 m/s$

Explanation:

As per the law of uncertainty we know that

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

now we know that

$\Delta x = 0.70 nm$

$m = 6.10 \times 10^{-25}$

also we have

$h = 6.626 \times 10^{-34} J.s$

now we will have

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

$(6.10 \times 10^{-25})\Delta v \times (0.70 \times 10^{-9}) = \frac{6.626 \times 10^{-34}}{4\pi}$

$\Delta v= 0.123 m/s$