Answer
Photons are emitted by the infrared lamp at a rate of $~~1.4\times 10^{21}~photons/s$
Work Step by Step
We can find the photon energy of a $700~nm$ photon:
$E = \frac{hc}{\lambda}$
$E = \frac{(6.63\times 10^{-34}~J\cdot s)(3.0\times 10^8~m/s)}{700\times 10^{-9}~m}$
$E = 2.84\times 10^{-19}~J$
We can find the rate at which photons are emitted:
$\frac{400~W}{2.84\times 10^{-19}~J/photon} = 1.4\times 10^{21}~photons/s$
Photons are emitted by the infrared lamp at a rate of $~~1.4\times 10^{21}~photons/s$
