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+//pagenumber 34 example 15
+clear
+nd=4*10^14;//atoms per cubic centimetre
+na=5*10^14;//atoms per cubic centimetre
+//(1) concentration
+ni=2.5*10^13;
+np=ni^2;
+//p1=n+10^14
+z=1;
+z1=10^14;
+u=-ni^2;
+n=poly([z z1 u],'q');
+roots(n);//n taken as 
+n=1.05*10^4;
+disp("concentration of the a free electrons   =   "+string((n)));
+p1=n+10^14;
+disp("concentration of the a free holes   =   "+string((p1)));
+//(2)
+disp("sample p");
+a=ni^2/(300^3*exp(-(0.785/0.026)));
+w=400;//kelvin
+ni=sqrt(a*w^3*exp(-0.786/(8.62*10^-5*w)));
+ni=((n)*(n+10^14))/10^3;
+n=ni-0.05*10^15;
+disp("n   =   "+string((n))+"electrons per cubic centimetre");
+p1=n+10^14;
+disp("p   =   "+string((p1))+"holes per cubic centimetre");
+
+
+disp("essentially intrinsic");
+
+