Can we draw the elctrons as pairs as shown...

documentclass[border=5mm]{standalone}

usepackage{bohr}

begin{document}

bohr{10}{P:10}

end{document}

A TikZ solution:

documentclass[tikz,border=5mm]{standalone}

begin{document}

begin{tikzpicture}

node[align=center,fill=black,circle] (o) at (0,0) {color{yellow}P:10\color{blue!50}N:10};

draw (0,0) circle (1.25cm) circle (2cm);

path[fill=red,draw=black] (90:1.25) circle (1.5mm);

path[fill=red,draw=black] (-90:1.25) circle (1.5mm);

path[fill=red,draw=black] (85:2) circle (1.5mm);

path[fill=red,draw=black] (95:2) circle (1.5mm);

path[fill=red,draw=black] (-85:2) circle (1.5mm);

path[fill=red,draw=black] (-95:2) circle (1.5mm);

path[fill=red,draw=black] (5:2) circle (1.5mm);

path[fill=red,draw=black] (-5:2) circle (1.5mm);

path[fill=red,draw=black] (175:2) circle (1.5mm);

path[fill=red,draw=black] (-175:2) circle (1.5mm);

end{tikzpicture}

end{document}

Edit 1:

We only have to define a new command. I can use newcommand but I prefer def because I can have that command in form of a TikZ command:

documentclass[tikz,border=5mm]{standalone}

begin{document}

begin{tikzpicture}

defpairelec[fill=#1,draw=#2,radius=#3] (#4:#5); {

    path[fill=#1,draw=#2] ({#4-5}:#5) circle (#3);

    path[fill=#1,draw=#2] ({#4+5}:#5) circle (#3);

}

node[align=center,fill=black,circle] (o) at (0,0) {color{yellow}P:10\color{blue!50}N:10};

draw (0,0) circle (1.25cm) circle (2cm);

path[fill=red,draw=black] (90:1.25) circle (1.5mm);

path[fill=red,draw=black] (-90:1.25) circle (1.5mm);

pairelec[fill=red,draw=black,radius=1.5mm] (0:2); 

% Remember fill -> draw -> radius - you must have all three options!

pairelec[fill=green,draw=blue,radius=1.5mm] (180:2);

pairelec[fill=white,draw=red,radius=1.5mm] (90:2);

pairelec[fill=yellow,draw=blue,radius=1.5mm] (-90:2);

end{tikzpicture}

end{document}

You can choose the fill color as well as the draw color and the radius.

Edit 2

At first I thought I would have to use maths, but I realize that I have intersections library :)

documentclass[tikz,border=5mm]{standalone}

usetikzlibrary{intersections}

begin{document}

begin{tikzpicture}

defpairelec[fill=#1,draw=#2,radius=#3] (#4:#5); {

    path[name path=cir] (0,0) circle (#5cm);

    path[name path=smallcir] (#4:#5) circle (#3);

    path[name intersections={of=cir and smallcir},fill=#1,draw=#2] (intersection-1) circle (#3) (intersection-2) circle (#3);

}

node[align=center,fill=black,circle] (o) at (0,0) {color{yellow}P:10\color{blue!50}N:10};

draw (0,0) circle (1.25cm) circle (2cm);

path[fill=red,draw=black] (90:1.25) circle (1.5mm);

path[fill=red,draw=black] (-90:1.25) circle (1.5mm);

pairelec[fill=red,draw=black,radius=1.5mm] (-8:2); 

% Remember fill -> draw -> radius - you must have all three options!

pairelec[fill=green,draw=blue,radius=3mm] (150:2.5);

pairelec[fill=white,draw=red,radius=1mm] (78:3);

pairelec[fill=yellow,draw=blue,radius=1.5mm] (-111:3.5);

end{tikzpicture}

end{document}

^{You may see the electrons are out of its orbits. This is for testing purpose only!}

Now, as far as I test, any sizes are okay. Please let me know if this doesn't work in some case.