Final answer:
To determine the number of photons emitted by the bulb during its lifetime, first calculate the total light energy output using the power and efficiency of the bulb. Then, find the energy of an individual photon based on its wavelength. Finally, divide the total light energy output by the energy of one photon.
Step-by-step explanation:
To solve the mathematical problem completely, let's first find out how much energy is converted into light energy by the bulb. The bulb consumes energy at a rate of 60 W (watts) and is 93% efficient in converting that energy to light energy.
Therefore, the energy converted to light per second is 0.93 × 60 W = 55.8 W. Over the lifetime of the bulb (730 hours), the total energy converted to light energy is 55.8 W × 730 h × 3600 s/h.
Now let's calculate the energy of a single photon. The energy (E) of a photon is given by the equation E = hc/λ, where h is Planck's constant (h = 6.626 x 10^-34 J·s), c is the speed of light in a vacuum (c = 3 x 10^8 m/s), and λ is the wavelength of the light (630 nm, which is 630 x 10^-9 m).
Substituting these values, we can determine the energy of one photon of wavelength 630 nm. The number of photons emitted by the bulb is then found by dividing the total energy converted to light by the energy of one photon.