The product of uncertainty in velocity and uncertainty in position of a micro particle of mass 'm' is not less than in which of the following?

Question

The product of uncertainty in velocity and uncertainty in position of a micro particle of mass 'm' is not less than in which of the following? (A) h × (3 π/m) (B) (h/3 π) × m (C) (h/4 π) × (1/m) (D) (h/4 π) × m

Tardigrade Admin · Accepted Answer

According to uncertainty principle, Δ p ⋅ Δ x ≥ (h/4 π) ...(i) Here, Δ p= uncertainty in momentum Δ x= uncertainty in position h= Planck's constant Since, p=m v Hence, Δ p=m Δ v Putting the value of Δ p in the expression m ⋅ Δ v × Δ x ≥ (h/4 π) Δ v × Δ x ≥ (h/4 π × m)

Q. The product of uncertainty in velocity and uncertainty in position of a micro particle of mass $^{'} m^{'}$ is not less than in which of the following?

$h \times \frac{3 π}{m}$

$\frac{h}{3 π} \times m$

$\frac{h}{4 π} \times \frac{1}{m}$

$\frac{h}{4 π} \times m$

Q. The product of uncertainty in velocity and uncertainty in position of a micro particle of mass ′m′ is not less than in which of the following?

h×m3π​

3πh​×m

4πh​×m1​

4πh​×m

According to uncertainty principle, Δp⋅Δx≥4πh​...(i) Here, Δp= uncertainty in momentum Δx= uncertainty in position h= Planck's constant Since, p=mv Hence, Δp=mΔv Putting the value of Δp in the expression m⋅Δv×Δx≥4πh​ Δv×Δx≥4π×mh​

Q. The product of uncertainty in velocity and uncertainty in position of a micro particle of mass $^{'} m^{'}$ is not less than in which of the following?

$h \times \frac{3 π}{m}$

$\frac{h}{3 π} \times m$

$\frac{h}{4 π} \times \frac{1}{m}$

$\frac{h}{4 π} \times m$