Calculate the uncertainty in velocity (Δv ) of a cricket ball (mass = 0.15 kg) if the uncertainty position (Δx ) is of the order of 1 Å (i.e. 10⁻¹⁰ m).
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use uncertainty principle,
e.g., ∆x.m∆v = h/4π
Here, ∆x is uncertainty in position
∆v is uncertainty in velocity.
Here, m = 0.15 kg , ∆x = 1 A° = 10⁻¹⁰ m
h = 6.626 × 10⁻³⁴ J.s
Now, ∆v = h/4πm∆x
= 6.626 × 10⁻³⁴/(4 × 3.14 × 0.15 × 10⁻¹⁰)
= 6.626 × 10⁻²⁴/(0.6 × 3.14)
= 3.51 × 10⁻²⁴ m/s
Hence, uncertainty in velocity = 3.51 × 10⁻²⁴ m/s
e.g., ∆x.m∆v = h/4π
Here, ∆x is uncertainty in position
∆v is uncertainty in velocity.
Here, m = 0.15 kg , ∆x = 1 A° = 10⁻¹⁰ m
h = 6.626 × 10⁻³⁴ J.s
Now, ∆v = h/4πm∆x
= 6.626 × 10⁻³⁴/(4 × 3.14 × 0.15 × 10⁻¹⁰)
= 6.626 × 10⁻²⁴/(0.6 × 3.14)
= 3.51 × 10⁻²⁴ m/s
Hence, uncertainty in velocity = 3.51 × 10⁻²⁴ m/s
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