Question

giving mathematical proof shows that electron cannot exist into the nucleus ​

Answer 1

Answer:

according to uncertainity principle

Δx Δp≥h/2π

for electron to exist on nuclues it should not exceed radius of nuclues

which is10^(-4)m/s

Δp≥h/(2π*10^(-4)

    ≥1.04*10^(-20)

since mass of electron is 9.1*10^(-31)

velocity=Δp/(9.1*10^(-31))

           =1.16*10^10m/s

if velocity of electron is 1.16*10^(-31) then

$m=\frac{m_{0}}{ \sqrt{1-\frac{v^{2} }{c^{2} }} }$

its mass will be imaginary which is not possible

so electron cannot exist into nuclues