Calculate the product of uncertainity in position and velocity for an electron of mass 9.1 x 10⁻³¹ kg according to Heisenberg uncertainty principle.
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According to Heisenberg's uncertainty principle,
∆x.m∆v = h/4π
so, ∆x.∆v = h/4πm
Hence, product of uncertainty in position and velocity = h/4πm
Here, m = 9.1 × 10⁻³¹ kg , h = 6.626 × 10⁻³⁴ J.s
Now, product of uncertainty in position and velocity = 6.626 × 10⁻³⁴/(4 × 3.14 × 9.1 × 10⁻³¹ )
= 6.626 × 10⁻³/(4 × 3.14 × 9.1)
= 0.0579 × 10⁻³ m²/s
= 5.79 × 10⁻⁵ m²/s
∆x.m∆v = h/4π
so, ∆x.∆v = h/4πm
Hence, product of uncertainty in position and velocity = h/4πm
Here, m = 9.1 × 10⁻³¹ kg , h = 6.626 × 10⁻³⁴ J.s
Now, product of uncertainty in position and velocity = 6.626 × 10⁻³⁴/(4 × 3.14 × 9.1 × 10⁻³¹ )
= 6.626 × 10⁻³/(4 × 3.14 × 9.1)
= 0.0579 × 10⁻³ m²/s
= 5.79 × 10⁻⁵ m²/s
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13
Answer:
5.78×10^(-5) m^(2)/second
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