Why electron cannot exist inside the nuc...

Why electron cannot exist inside the nucleus according to Heisenberg's uncertainty principle?

Text Solution

Verified by Experts

Diameter of the atomic nucleus is of the order of `10^(-15) m`
`:.` The maximum uncertainity in the position of electron is `10^(-15)` m
Mass of electron `= 9.1xx 10^(-31) kg`
Now,
`Deltax .Deltap = ( h)/( 4pi)`
`Deltax xx ( mDeltav )= ( h)/( 4pi)`
`Deltav = ( h)/( 4pi) xx (1 )/(Deltax-m)= ( 6.26 xx 10^(-34))/( 4 xx ((22)/( 7)))xx ( 1)/( 10^(-15) xx 9.1xx 10^(-31))`
`Deltav = 5.80 xx 10^(10) ms^(-1)`
This value is much higher than the velocity of light and hence,it is not possible.

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`Delta x xx Delta p = (h)/(6 pi)`

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`lambda = ( h)/( mv)`

`Deltax xx Deltap ge ( h)/( 4pi)`

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`mvr = n (h)/(2pi)`

Which of the following is Heisenberg uncertainty principle?

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