[marikas]

4. The Boltzmann equation for a two-level system is shown below:

equitation 2.    n2/n1= e−ΔE/kBT
where n1 is the number of molecules in the lower state, n2 is the
number of molecules in the upper state, and ΔE is the energy
difference between them. kB is Boltzmann’s constant and T is
the temperature. The total number of molecules, n is given

equitation 3.    n = n1 + n2

By rearranging Equations 2 and 3, show that the fraction of
molecules in the lower state, n1/n, is given by the following
expression:
n1/n= (eΔE/kBT/1 + eΔE/kBT )

[Yggdrasil]

Please read the Forum Rules.  You should that show you've at least attempted to answer the problem before we will help you.

Where specifically are you having problems.  It seems like a very straightforward derivation.

[marikas]

do you think i have not tried it i did. but no good results perhaps some tips you coul give me. please

[Yggdrasil]

Using eq 2, solve for n2.  Plug this into the eq 3 and solve for n1/n.  This will give you 1/(e^-ΔE/kT+1) which can be easily changed into the form you want.