Answer
7
Work Step by Step
We know that
$\frac{1}{\lambda}=\frac{1}{400nm}(R)(\frac{1}{2^2}-\frac{1}{n^2})$
$\frac{1}{n^2}=\frac{1}{2^2}-\frac{1}{(400nm)(R)}$
$\frac{1}{n^2}=\frac{1}{4}-\frac{1}{(400\times 10^{-9})(1.097\times 10^7)}$
$\frac{1}{n^2}=0.0221$
$n=\sqrt{\frac{1}{0.0221}}=7$