Answer to Question #301645 in Quantum Mechanics for Bunty

Question

Using uncertainty principle show that an electron can't stay inside the nucleus . Radius of nucleas =5 ×10^-15

Answer 1

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

= 9.1x 10^(-31) kg

Now,

∆x .∆p = ( h)/( 4pi)

∆x ( m∆v )= ( h)/( 4pi)

∆v = ( h)/( 4pi) x (1 )/(∆xm),

∆v = 5.80 x10^(10) ms^(-1)

This value is much higher than the velocity of light and hence, it is not possible.