How many photons of frequency 2.7*10^14 Hertz would be needed to light a 60 Watt light bulb for 1hr?
1 watt = 1 J/second.
60 watts is 60 J/second and that for 1 hour is 60 x (60sec/min) x (60min/hour) = 216,000 J/hour is the energy needed to power the bulb.
E of photon = Planck's constant x 2.7E14 = ??
Divide the power needed by the power/photon to find the number of photons. Surprise. It's a huge number.
To determine the number of photons required to light a 60 Watt light bulb for 1 hour, we need to follow a few steps.
First, we need to calculate the energy of one photon. The energy of a photon can be found using the formula:
E = h * ν
where E is the energy of the photon, h is Planck's constant (approximately 6.626 x 10^-34 J·s), and ν (nu) is the frequency of the photon. In this case, the frequency is given as 2.7 x 10^14 Hz.
Using the formula, we can calculate the energy of one photon:
E = (6.626 x 10^-34 J·s) * (2.7 x 10^14 Hz)
E = 17.8572 x 10^-20 J
Next, we need to determine the total energy consumed by the 60 Watt light bulb over the course of 1 hour. Power (P) is defined as the rate at which energy is consumed, and is calculated using the formula:
P = E / t
where P is power, E is energy, and t is time.
Substituting the given values, we have:
60 W = E / (1 hour)
To calculate the energy consumed by the light bulb, we multiply power by time:
E = (60 W) * (3600 s)
E = 216000 J
Finally, we can calculate the number of photons required by dividing the total energy consumed by the energy per photon:
Number of photons = E / (energy per photon)
Substituting the given values, we get:
Number of photons = 216000 J / (17.8572 x 10^-20 J)
Calculating the above expression, we find:
Number of photons ≈ 1.208 x 10^24 photons
Therefore, approximately 1.208 x 10^24 photons of frequency 2.7 x 10^14 Hz would be needed to light a 60 Watt light bulb for 1 hour.