I want to solve the equation (iv) as a function of E0 as shown in the attached picture. I tried to calculate it using the following code. I am stuck in this problem! please help

if true
  % code
end
r=5*10^-9;
V=4/3*pi*r^3;
Nd=10^17;
E0=19;
Ld=18.5*10^-9;
E=E0+1/6*(r/Ld)^2;
Nr=Nd*exp(-(E0+(1/6)*(r/Ld)^2));
eqn=Nd-Nd*exp(-(E0+(1/6)*(r/Ld)^2));
syms E0
eqn=Nd-Nd*exp(-(E0+(1/6)*(r/Ld)^2));
int(eqn,[0,4/3*pi*r^3])

[Torsten]

I wonder why your integration is over E0 and not over R:

syms R
eqn = (Nd-Nd*exp(-(E0+(1/6)*(R/Ld)^2)))*4*pi*R^2;
sol = int(eqn,R,0,r)

Answer 1

[madhan ravi]

r=5*10^-9;
V=4/3*pi*r^3;
Nd=10^17;
E0=19;
Ld=18.5*10^-9;
E=E0+1/6*(r/Ld)^2;
Nr=Nd*exp(-(E0+(1/6)*(r/Ld)^2));
eqn=Nd-Nd*exp(-(E0+(1/6)*(r/Ld)^2));
syms E0
eqn=Nd-Nd*exp(-(E0+(1/6)*(r/Ld)^2));
int(eqn,[0,4/3*pi*r^3]) %no errors occurred

[Anil Kumar]

@Madhan ravi, I am getting the following error Error using mupadmex Error in MuPAD command: The second argument must be of form x or x = a..b. [int]

Error in sym/int (line 107) rSym = mupadmex('symobj::intindef',f.s,x.s,options);

Error in grainsize2310_3 (line 11) int(eqn,[0,4/3*pi*r^3])