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If an electron is moving with a velocity...

If an electron is moving with a velocity `600ms^(-1)` which is accurate upto 0.005% then calculate the uncertainty in its position. ( `h = 6.63 xx 10^(-34) Js`. Mass of electron `= 9.1 xx 10^(-31) kg )`.

Text Solution

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Velocity of the electon `= 600 ms^(-1)`
Uncertainty in velocity ` = ( 0 .005 )/( 100 ) xx 600 ms^(-1) = 0.03 ms^(-1)`
`= 3 xx 10^(-2) ms^(-1)`
Now, `( Delta x ) ( m Delta v) `
`= ( h )/( 4pi ) `
`:. Delta x = ( h )/( 4pi. m. Delta v)`
`= ( 6.626 xx 10^(-34) kg m^(2) s^(-1))/( 4 xx 3.14 xx9.1 xx 10^(_31) kg xx 3 xx 10^(-2) ms^(-1))`
`= 1.93 xx 10^(-3) m`
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