Question

why the existence of electron is not in nuclear of orbit

Answer 1

According to the general theory of relativity, we know that no object having mass can travel faster than light in space. We will be using this key point and the Heisenberg’s uncertainity principle to answer your question.

According to the Heisenberg’s uncertainity principle,

It is impossible to simultaneously determine the postion and momentum(velocity) of an electron with great accuracy.

Numerically, If we consider ΔvΔv to be the uncertainity in velocity ,ΔpΔp to be the uncertainity in momentum, ΔxΔx to be uncertainity in position and hh to be the planck’s constant (6.626∗10−34Js),6.626∗10−34Js),

The above law can be expressed numerically as

ΔxΔp≥h4πΔxΔp≥h4π

Where m is the mass of electron,

Substituting, p=mvp=mv we get,

ΔxΔv≥h4πmΔxΔv≥h4πm

Now, if we consider the radius of the atomic nucleus to be 10−15m10−15m and mass of electron, ′m′′m′to be 9.1∗10−319.1∗10−31 kg, we get

10−15Δv≥6.626∗10−344∗3.14∗9.1∗10−3110−15Δv≥6.626∗10−344∗3.14∗9.1∗10−31

Δv≥6.626∗10−344∗3.14∗9.1∗10−31∗10−15Δv≥6.626∗10−344∗3.14∗9.1∗10−31∗10−15

Δv≥5.79∗1010Δv≥5.79∗1010 m/s

Calulating ΔvΔv, we get a value of

5.79∗10105.79∗1010 m/s which contradicts the theory of relativity. What this means is that if an electron exists in the nucleus, it has to travel with a speed of 5.79∗10105.79∗1010 m/s. An object can only travel faster than light if it has no mass but electrons do have mass, hence they can’t travel faster than the speed of light which is precisely 299,792,458299,792,458 m/s.

Hence, an electron can’t exist in the nucleus.