The uncertainties in the velocities of two particles, A and B are 0.05 and 0.02 ms -1, respectively. The mass of B is five times to that of the mass of A. What is the ratio of uncertainties ((Δ xA/Δ xB)) in their positions?

Question

The uncertainties in the velocities of two particles, A and B are 0.05 and 0.02 ms -1, respectively. The mass of B is five times to that of the mass of A. What is the ratio of uncertainties ((Δ xA/Δ xB)) in their positions? (A) 2 (B) 0.25 (C) 4 (D) 1

Tardigrade Admin · Accepted Answer

According to Heisenberg Δ x × m Δ v-(h/4 π) For particle A Δ x =Δ xA m =m Δ v =0.05 So, Δ xA × m × 0.05=(h/4 π) ... (i) For particle B Δ x =Δ xB m =5 m Δ v =0.02 So, Δ xB × 5 m × 0.02=(h/4 π) ... (ii) Eq. (i)/(ii), we get (Δ xA/Δ xB)=2 .

Q. The uncertainties in the velocities of two particles, A and B are 0.05 and 0.02ms−1, respectively. The mass of B is five times to that of the mass of A. What is the ratio of uncertainties (ΔxB​ΔxA​​) in their positions?

2

0.25

4

1

According to Heisenberg Δx×mΔv−4πh​ For particle A Δx=ΔxA​ m=m Δv=0.05 So, ΔxA​×m×0.05=4πh​ ... (i) For particle B Δx=ΔxB​ m=5m Δv=0.02 So, ΔxB​×5m×0.02=4πh​ ... (ii) Eq. (i)/(ii), we get ΔxB​ΔxA​​=2.

Q. The uncertainties in the velocities of two particles, $A$ and $B$ are $0.05$ and $0.02 m s^{- 1}$ , respectively. The mass of $B$ is five times to that of the mass of $A$ . What is the ratio of uncertainties $(\frac{Δ x _{A}}{Δ x _{B}})$ in their positions?