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Calculate the uncertainty in position of...

Calculate the uncertainty in position of an electron if the uncertainty in its velocity is `5.7 xx 10^(5) m s^(-1), h = 6.6 xx 10^(-34) kg m^(2) s^(-1)` mass of electron `= 9.1 xx 10^(-31) kg `

Text Solution

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According to Heisenberg.s uncertainty principle,
`Delta x xx Delta p ge h/(4 pi) "or" Delta x xx mDelta v ge h/(4pi)`
`:. Delta x ge h/(4 pi m Delta v)`
` Delta v = 5.7 xx 10^5 m s^(-1), m = 9.1 xx 10^(-31) kg`,
`h = 6.6 xx 10^(-34) J s`
`:. Delta x = (6.6 xx 10^(-34) kg m^2 s^(-1))/(4 xx 3.142 xx (9.1 xx 10^(-31) kg) xx (5.7 xx 10^5 ms^(-1)))`
`= 1.012 xx 10^(-10) m`.
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