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Calculate the uncertainty in the positio...

Calculate the uncertainty in the position of an electron if the uncertainty in its velocity is `5.7 xx 10^5 m//sec (h = 6.626 xx 10^(-34) kg m^2 s^(-1)` , mass of the electron `= 9.1 xx 10^(−31) kg` ).

Text Solution

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Here we are given
`Delta v = 5.7 xx 10^5 ms^(-1)`
`m = 9.1 xx 10^(-31) kg `
`h = 6.626 xx 10^(-34) kg m^2 s^(-1)`
Substituting these values in the equation for uncertainty principle
`Delta x xx (m xx Delta v) = (h)/(4pi)`
we have `Delta x = (h)/(4pi xx m xx Delta v)`
` = (6.626 xx 10^(-34))/(4 xx 22/7 xx 9.1 xx 10^(-31) xx 5.7 xx 10^5)`
` =1.0 xx 10^(-10) m`
Uncertainly in position ` = pm 10^(-10) m`
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