The uncertainty in position is $10^{-10} \ m$ and in velocity is $5.27 \times 10^{-24} \ m \ s^{-1}$. Calculate the mass of the particle.
(0.1 KG) According to Heisenberg's uncertainty principle,$\Delta x \cdot m \Delta v \geq \frac{h}{4 \pi}$.
Rearranging for mass $(m)$:
$m = \frac{h}{4 \pi \Delta x \cdot \Delta v}$
Given:
$h = 6.626 \times 10^{-34} \ J \ s$
$\Delta x = 10^{-10} \ m$
$\Delta v = 5.27 \times 10^{-24} \ m \ s^{-1}$
Substituting the values:
$m = \frac{6.626 \times 10^{-34}}{4 \times 3.14159 \times 10^{-10} \times 5.27 \times 10^{-24}}$
$m = \frac{6.626 \times 10^{-34}}{6.626 \times 10^{-33}}$
$m = 0.1 \ kg$
Rearranging for mass $(m)$:
$m = \frac{h}{4 \pi \Delta x \cdot \Delta v}$
Given:
$h = 6.626 \times 10^{-34} \ J \ s$
$\Delta x = 10^{-10} \ m$
$\Delta v = 5.27 \times 10^{-24} \ m \ s^{-1}$
Substituting the values:
$m = \frac{6.626 \times 10^{-34}}{4 \times 3.14159 \times 10^{-10} \times 5.27 \times 10^{-24}}$
$m = \frac{6.626 \times 10^{-34}}{6.626 \times 10^{-33}}$
$m = 0.1 \ kg$
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