Calculate the product of uncertainty in displacement and velocity for an electron of masss `9.1xx10^(-31)`kg according to Heisenberg's uncertainty principle.

Explanation

According to Heisenberg.s uncertainty principle,
`Delta x xx Delta p ge h/(4pi)`
or `" " Delta x xx m Delta v ge h/(4pi) " " ( :. ` m is constant)
or `Delta x xx Delta v ge h/(4 m pi)`
`m = 9.1 xx 10^(-31) kg, h = 6.6 xx 10^(-34) kg m^2 s^(-1), pi = 3.14`
`:. Delta x xx Delta v ge (6.6 xx 10^(-34) kg m^2 s^(-1))/(4 xx (9.1 xx 10^(-31) kg) xx 3.14)`
or `" " Delta x xx Delta v ge (6.6)/(4 xx 9.1 xx 3.14) xx 10^(-3) m^2 s^(-1)`
or `" " Delta x xx Deltav ge 5.77 xx 10^(-5) m^2 s^(-1)`
Thus, product of uncertainties in position and velocity of an electron is equal to or greater than `5.77 xx 10^(-5) m^2 s^(-1)`.