Question

According to Heinsbergs the principal, the product of uncertainty is position and velocity for an electron of mass -31

9.1×10

-3 -5 -5 -6

(a) 2.8×10 (b) 3.8×10 (c)5.8×10 (d)6.8×10

How to solve it

Answer 1

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According to Heisenberg's uncertainty principle,
∆x.m∆v = h/4π
so, ∆x.∆v = h/4πm
Here ∆x=change in position
∆v=change in velocity
Hence, product of uncertainty in position and velocity = h/4πm
Here, given that
m = 9.1 × 10⁻³¹ kg
​​​​​​ h = 6.626 × 10⁻³⁴ J.s (it is standard value)
Now answer is
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