Answer
$3.16\times10^{-34}kg \cdot m^2/s$.
Work Step by Step
Use the energy to calculate n for this state.
$$E_n=-\frac{-13.6eV}{n^2}$$
$$-1.51eV=-\frac{-13.6eV}{n^2}$$
$$n=3$$
Now use the Bohr equation to calculate L.
$$L=n\hbar=3.16\times10^{-34}kg \cdot m^2/s $$
In Section 41.3, we will find that the modern quantum mechanical model gives a slightly different result.
