Kushagra Madhukar
Last Activity: 5 Years ago
Hello student
One anology for this can be if electron were to exist inside nucleus they will get annihilated very quickly due to the presence of positively charged proton to form a neutron, and thus the elctrons wouldn’t be able to exist freely as we know it for long duration of time along with the existence of protons around us.
Another method could be used to neumerically prove the same on the basis of Heisenberg’s uncertainity principle.
As we know atomic nucleus is of the order 10-15m
For an electron to exist inside nucleus its uncertainity in position should be -15m
nom mass of electrom = 9.1 x 10-31 kg
Hence, by Heisenberg uncertainity principle
Δx.Δp >= h/4π
v >= h/(4πΔx.m)
= 6.626 x 10-34 / ( 4 x 3.14 x 10-15 x 9.1 x 10-31)
= 5.79 x 1010m/s
Hence the uncertainity in its velocity will be 5.79 x 1010m/s which is very much greater than even the speed of light
and as we know nothing in this universe travels faster than light, it is impossible for an electron to have this much uncertainity in its velocity.
Hence, our assumption that electron exist inside the nucleus must be wrong.
Hope it helps
Regards,
Kushagra