Expression substitution

Question

I konw: $$ a_0=\frac{4 \pi \epsilon_0 \hbar^2}{m_e e^2} $$ and $$ \alpha = \frac{m_{\mathrm{e}}^2 e^4}{18 \pi^3 \epsilon_0^2 \hbar^4} $$

So we can use $a_0$ for $\alpha$,like this: $$ \alpha=\frac{m_{\mathrm{e}}^2 e^4}{18 \pi^3 \epsilon_0^2 \hbar^4}=\frac{16}{18 \pi} \cdot \frac{m_{\mathrm{e}}^2 e^4}{16 \pi^2 \epsilon_0^2 \hbar^4}=\frac{8}{9 \pi} \cdot \frac{1}{a_0^2} $$

alpha = (e^4 me^2)/(18 eps^2 h^4 \[Pi]^3);
a0 = (4 Pi eps h^2)/(me e^2);

I've tried a few things and failed. What should I do

Answer 1

eq1 = alpha == (e^4 me^2)/(18 eps^2 h^4 \[Pi]^3);
eq2 = a0 == (4 Pi eps h^2)/(me e^2);

Solve[{eq1, eq2}, alpha, {e}]