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why electron cant exist in nucleus with explanation
I will explain you in easiest way.
(1) NUCLEAR SIZE : typically nuclei are less than 1 Fermi metre ( ≈10-¹⁴m approximately) in radius . If an electron exists inside a nucleus , the uncertainty in it's position (∆x ) may not exceed 10-¹⁴m . According to hinsenberg's uncertainty principle , uncertainty in electron moment is
∆p ≥ (h/2π) / ∆x
Putting the value of the constant we get
∆p ≥ 1.054 × 10 -³⁴ / 10-¹⁴
Solving we get ∆p ≥ 1.1× 10^-20 kg ms-¹
If this is the uncertainty in the electron's momentum , the momentum itself must be at least comparable in magnitude.
•: approximate momentum of the electron = p= 1.1 × 10 ^ -20 kg ms-¹. An electron whose momentum is 1.1×10^-20 kg ms-¹ has a K.E ( T) many times greater than it's rest energy m'c² .i.e T »m’c² . Hence we can use the extreme relativistic formula.
T= (1.1×10^-20)× (3×10^8) = 3.3 × 10 -¹² J
Or 20.63 Mev
This shows that if an electron exists in the nucleus , the K.E. of the electron must be more than 20 Mev . Electron of such large energy are never found to be emitted during beta - decay . The maximum energy of a beta- particle emitted is only 2 to 3 Mev hence we can concluded that electron cannot be present within the nuclei.
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