Answer
$21.6mJ$
Work Step by Step
First of all, we find the energy of a light bulb as:
$W_{bulb}=Pt$
We plug in the known values to obtain:
$W_{bulb}=(60W)(24h\times 3600s/h)$
$W_{bulb}=5.18\times 10^6J$
Now, we can find the required energy to run an atomic clock for one day:
$W_{atoms}=\frac{W_bulb}{240\times 10^6}$
$W_{atoms}=\frac{5.18\times 10^6}{240\times 10^6}$
$W_{atoms}=21.6mJ$