Suppose n_r and n_b represent the number of photons emitted by a...

The energy of a single photon is given by $E = \dfrac{hc}{\lambda}$, where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength.

The total energy emitted by a bulb of power $P$ in time interval $t$ is $E_{total} = P t$.

The number of photons emitted in time $t$ is $n = \dfrac{E_{total}}{E} = \dfrac{P t \lambda}{hc}$.

Since the power $P$ and time interval $t$ are the same for both bulbs, the number of photons emitted is directly proportional to the wavelength of the light, i.e., $n \propto \lambda$.

The wavelength of red light is greater than the wavelength of blue light ($\lambda_r > \lambda_b$).

Therefore, the number of photons emitted by the red bulb is greater than the number of photons emitted by the blue bulb, which gives $n_r > n_b$.