The uncertanities in then velocities of two particle A and B are 0.05 and 0.02`ms^(-1)` respectively.The mass of B is five times to that of A.What is the ratio of uncertainities `[(Delta x_(A))/(Delta x_(B))]`in their positions?

Options

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

Answer

a

Explanation

Velocity of particle,`A=0.05 ms^(-1)`
Velocity of particle,`B=0.02 ms^(2)` Mass of particle ,`B=5m_A`
Heisenberg.s uncertainity equation is given by,
`Delta x xxDelta vxxm=h/(4pi)`
`Deltax_Axx0.05xxm_A=h/(4pi)`
`Delta x_Axx0.02xx5m_A=h/(4pi)`
From equation (1) and (2) we get
`Delta x_Axx0.05m_A=Delta x_Bxx0.10 m_A`
`(Delta x_A)/(Delta x_B)=(0.10 m_A)/(0.05m_A)=2`