Fix a formula with fraction 1/2 in subscript mode

The digit 1 is much thinner than the other digits. Most fonts, however, define it with a bounding box equal to the ones for the other digits, for the sake of alignment in tables.

You can solve the special case by defining a suitable command:

\documentclass{article}
\usepackage{newtxtext,newtxmath}

\newcommand{\one}{\mspace{-1mu}1\mspace{-1.5mu}}

\begin{document}

\begin{equation}
T_{\one/2}=\frac {\ln 2}{\lambda}=\tau \ln 2<\tau
\end{equation}

\begin{equation}
N(t)=N_0e^{-\frac{t\ln 2}{T_{\one/2}}}=
N_0e^{\ln 2^{-\frac t{T_{\one/2}}}}=N_0{2}^{-\frac{t}{T_{\one/2}}}
\end{equation}

\end{document}

I wouldn't touch the slash.

I would also omit the step with the fraction at second level superscript: it is unreadable and actually an easy application of logarithms. A short explanation after the equation is more than sufficient.