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 A. What is the ratio of uncertainties `((Delta_(X_A))/(Delta_(X_B)))` in their positions

Options

A. 2
B. 0.25
C. 4
D. 1

Answer

A

Explanation

According to Heisenberg
`DeltachixxmDeltav=h/(4pi)`
For particle A
`Deltachi=Deltachi_(A),m=m,Deltav=0.05`
So, `Deltachi_(A)xxmxx0.05=h/(4pi)" "...(i)`
For particle B
`Deltachi=Deltachi_(B),m=5m,Deltav=0.02`
So `Deltachi_(B)xx5mxx0.02=h/(4pi)" "...(ii)`
Eq. (i)/(ii), we get
`(Deltachi_(A))/(Deltachi_(B))=2`.