Answer
$a) \space N = 3.52 \times 10^{17} \space photons/sec$
$b) \space N = 3.52 \times 10^{18} \space photons/sec$
Work Step by Step
Power is energy emitted per unit time i.e $P = {E\over t}$
Consider $t = 1 second$
$\therefore P = E = {Nhc\over \lambda}$
where $N$ is the number of photons emitted in one second and $\lambda = 700nm$
Hence,
$$N = {P\lambda \over hc}$$
$(a)\space P = 0.1W$
$N = {0.1 \times 700 \times 10^{-9} \over 6.626\times 10^{-34} \times 3 \times 10^8} =3.52\times 10^{17}$
$(b)\space P = 100W$
$N = {1 \times 700 \times 10^{-9} \over 6.626\times 10^{-34} \times 3 \times 10^8} =3.52\times 10^{18}$
