The product of uncertainty in the position and uncertainty in velocity of a particle is `5.79 xx 10^(-5) m^2 s^(-1)`.
If uncertainty in the position is 1 nm , what is the uncertainty in the measurement of its velocity in `m s^(-1)` ?

Options

A. `5.79 xx 10^7`
B. `5.79 xx 10^5`
C. `5.79 xx 10^(-5)`
D. `5.79 xx 10^4`

Answer

D

Explanation

According to Heisenberg's uncertinity principle:
`Deltax.Deltavgt=h/(4pim)`
where, `Deltax` = incertinity in position
h = Planck's constant
Given, the product of uncertinity in the position
and uncertinity in velocity of a particle is
`579xx10^(-5)m^2s^(-1)."It means"Deltax.Deltav=579xx10^(-5)m^2s^(-1)`
Also, uncertinity in the position is 1 nm
`:.10^(-9)mxxDeltav=579xx10^(-5)m^2s^(-1)" "( :' 1nm=10^(-9)m)`
`"or, "Deltav=(579xx10^(-5)m^2s^(-1))/(10^(-9)m)=579xx10^4ms^(-1)`