The uncertainty in position of the alpha particle is 1.79 x [tex]10^{-3}[/tex] m
Given that an alpha particle is emitted by a Radium isotope.
Mass of the alpha particle, m = g
Velocity of the alpha particle, v = 3.4 x 10⁷ ± 0.1 x 10⁷ mi/h.
So the error in the measurement of velocity, Δv = 0.1X10⁷ mi/h.
= 0.44704 x 0.1 x10⁷ m/s
= 0.044704 x 10⁷ m/s
Now by Heisenberg's Uncertainty principle,
[tex]\Delta x\times m\Delta v=\frac{h}{4\pi}[/tex] , where h = [tex]6.626\times10^{-34}[/tex] Js
So the uncertainty in position , Δx = [tex]\frac{h}{4\pi\times m\Delta v}[/tex]
= [tex]\frac{6.626\times10^{-34}}{4\times 3.14 \times 6.6\times 10^{-24}\times 0.044704 \times 10^7}[/tex]
=1.79 x [tex]10^{-3}[/tex] m
Learn more about Heisenberg's Uncertainty principle at https://brainly.com/question/16941142
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