Question

If 5% of the energy supplied to an incandescent light is radiated as visible light, how many visible quanta are emitted per second by a small 10-watt bulb? Assume the wavelength of the light to be 520 nm.

Answer 1

To calculate the number of visible photons emitted by a 10-watt bulb per second, we first determine the energy per photon for the given wavelength of 520 nm. We then find the power devoted to visible light, which is 5% of the total power of the bulb. Dividing this power by the energy per photon gives us the number of photons emitted per second.

Step-by-step explanation:

To calculate the number of visible quanta, or photons, emitted per second by a 10-watt incandescent bulb, where 5% of the energy is radiated as visible light, we can use the concept that power is energy per unit time.

First, we need to find the energy per photon using the wavelength given (520 nm) and the energy per photon formula:

E = ℃

Where:

E is the energy per photon,

℃ is Planck's constant (6.63 × 10-34 J·s),

c is the speed of light (3.00 × 108 m/s),

λ is the wavelength of the light (520 nm).

Substitute the values:

E = (6.63 × 10-34 J·s) (3.00 × 108 m/s) / (520 × 10-9 m)

Next, calculate the total energy emitted as visible light per second (power visible):

Power visible = Total power × Percentage of visible light

For a 10-watt bulb:

Power visible = 10 W × 0.05

Power visible = 0.5 W (which is equivalent to 0.5 J/s)

Finally, divide the power visible by the energy per photon to find the number of photons emitted per second:

Number of photons/second = Power visible / E