Issue with using Farad units and final computation

Questions
1

Hello, not sure if this computation is correct.? Not sure how to define the Farad units.
8.854*10^-12"Farads"]*m^-1 ; (would this be correct?)

Any help will be appreciated. Thanks.

Clear["Global`*"]
T = Quantity[1000, "Kelvins"];
kb = Quantity[1, "BoltzmannConstant"];
n = 10^11 m^3 ;
v = 2* 10^4;
\[Epsilon] = Quantity[ 8.854, "Farads"]^ ;
(*\[Epsilon] = Quantity[ 8.854*10^-12"Farads"]*m^-1 ;*)
e = 1.6 * 10^-19; 
N[LD = ((\[Epsilon] kb T)/(n (e)^2))^0.5]
2

Do you mean

n = Quantity[10^11 , "Meters"^3];
\[Epsilon] = Quantity[8.854, "Farads"/"Meters"];

Instead of ^0.5 I would recommend ^(1/2) or Sqrt.

3

Thanks for your reply. I’m still getting some weird results. No sure how to set units to get a numerical value. Can you provide me any clue? Thanks once again

T = Quantity[190, "Kelvins"];
kb = Quantity[1, "BoltzmannConstant"];
n = Quantity[10^11, "Meters"^3];
\[Epsilon] = Quantity[8.854 *10^-12, "Farads"/"Meters"];
e =  Quantity[1.60 *10^-19, "Coulombs"];

N[LD = ((kb T \[Epsilon])/(e^2 n))^(1/2)]

N[ND = 4 \[Pi]/(3 n (LD)^3)]

Quantity[8.1063710^8, (
Sqrt[“BoltzmannConstant”] Sqrt[“Farads”] Sqrt[“Kelvins”])/(
“Coulombs” (“Meters”)^2)]
Quantity[
7.8633710^-38, ((“Coulombs”)^3 (“Meters”)^3)/((
“BoltzmannConstant”)^(3/2) (“Farads”)^(3/2) (“Kelvins”)^(3/2))]

4

Those N[ ] serve no purpose, because the numbers are already floating-point. By “numerical value” do you mean this?

LD = ((kb T \[Epsilon])/(e^2 n))^(1/2)
QuantityMagnitude[LD]