# why electron cant exist in nucleus with explanation

420 Points
13 years ago

Dear Baba

On the basis of Heisenberg's uncertainty principle, it can be shown as to why electron cannot exist within the atomic nucleus. The radius of the atomic nucleus is of the order of 10-15 m. Now, if the electron were to exist within the nucleus, then the maximum uncertainty in its position would have been 10-15 m.

Mass of electron, m = 9.1 x 10-31 kg, Dx =1 x 10-15 m.

The value of uncertainty in velocity, Dv is much higher than the velocity of light (3.0 x 108 ms-1) and therefore, it is not possible. Hence an electron cannot be found within the atomic nucleus.

All the best
AKASH GOYAL
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sunil sahu
36 Points
13 years ago

hi garg

because if you consider the electron in nucleus it will be the thomsons model and this model cannot explain the stability of atom and also the advantages of bohr's model

utkarsh
11 Points
7 years ago
well the maximum energy of emission of em waves from the atom(like beta rays) is 7MeV.if the electron were to exist in the nucleus,then the energy of the electron would become around 20MeV,which means that the energy of the emission show be higher.so electrons can’t exist in nucleus,all this data is experimental.
15 Points
5 years ago
Let us assume that an electron can exist inside the nucleus.
Then the total spin of the nucleus will be half integral if there are three Fermioms can exist inside the nucleus.
For example,consider the deuteron(nucleus of deuterium)having one proton,one neutron and and electron,then total spin of the nucleus is 3/2(1/2+1/2+1/2=3/2).
But experiments shows that spin of the deuteron nucleus is +1.Hence only two fermions can exist inside the nucleus in deuteron.
#No electron can exist inside the nucleus#

3 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