Answer
The ratio of the red laser's photon emission rate to blue laser's photon emission rate is $~~1.44$
Work Step by Step
We can write an expression for the energy of each photon:
$E = \frac{h~c}{\lambda}$
We can write an expression for the photon emission rate:
$R = \frac{P}{E}$
$R = \frac{P~\lambda}{h~c}$
We can find the ratio of the red laser's photon emission rate to blue laser's photon emission rate:
$\frac{R_r}{R_b} = \frac{\frac{P~\lambda_r}{h~c}}{\frac{P~\lambda_b}{h~c}}$
$\frac{R_r}{R_b} = \frac{\lambda_r}{\lambda_b}$
$\frac{R_r}{R_b} = \frac{650~nm}{450~nm}$
$\frac{R_r}{R_b} = 1.44$
The ratio of the red laser's photon emission rate to blue laser's photon emission rate is $~~1.44$
