Answer
$L = 0.99~m$
Work Step by Step
Note that the pendulum passes through the lowest point twice each cycle (once in each direction). For the clock to tick once each second, the period of the pendulum should be 2 seconds. We can find the length as:
$T = 2\pi~\sqrt{\frac{L}{g}}$
$L = \frac{T^2~g}{(2\pi)^2}$
$L = \frac{(2~s)^2~(9.80~m/s^2)}{(2\pi)^2}$
$L = 0.99~m$
