A 32 W (1 W = 1 J/s) lamp generates violet light at a wavelength of 420 nm. How many photons of this light will the lamp generate in 2.0 s?
I am a little confused on how you got 5E-19 J
Why did the lamp start telling jokes? Because it heard you're a fan of light humor!
To calculate the number of photons generated by the lamp, we can use the formula:
Number of photons = (Power / Energy of one photon) x Time
The energy of one photon can be calculated using the equation:
Energy of one photon = Planck's constant x Speed of light / Wavelength
So let's plug in the values and do the math!
Energy of one photon = (6.626 x 10^-34 J.s) x (3 x 10^8 m/s) / (420 x 10^-9 m)
Energy of one photon = (1987.6 x 10^-26 J.m) / (420 x 10^-9 m)
Energy of one photon = 0.0047324 x 10^-17 J
Now let's calculate the number of photons:
Number of photons = (32 W / 0.0047324 x 10^-17 J) x 2.0 s
Oops, seems like I made a miscalculation! But don't worry, I'm just a clown bot, not an expert in physics. Let's try to resolve this issue in a more "enlightening" way.
To find the number of photons generated by the lamp, we need to use the equation:
Number of photons = Energy / Energy per photon
First, let's calculate the energy of the light generated by the lamp. We can use the equation:
Energy = Power x Time
Given that the lamp has a power of 32 W and it operates for 2.0 s, we can calculate the energy as follows:
Energy = 32 W x 2.0 s
= 64 J
Now, let's calculate the energy per photon using the equation:
Energy per photon = Planck's constant x Speed of light / Wavelength
Planck's constant, denoted by h, is 6.626 x 10^-34 J·s, and the speed of light, denoted by c, is approximately 3.0 x 10^8 m/s. The wavelength, denoted by λ, is given as 420 nm, which we need to convert to meters:
Wavelength = 420 nm x (1 m / 10^9 nm)
= 420 x 10^-9 m
= 4.2 x 10^-7 m
Using these values, we can calculate the energy per photon as follows:
Energy per photon = (6.626 x 10^-34 J·s) x (3.0 x 10^8 m/s) / (4.2 x 10^-7 m)
= 4.749 x 10^-19 J
Now, we can calculate the number of photons generated by the lamp using the equation:
Number of photons = Energy / Energy per photon
Number of photons = 64 J / (4.749 x 10^-19 J)
= 1.347 x 10^20 photons
Therefore, the lamp will generate approximately 1.347 x 10^20 photons of violet light in 2.0 s.
The first two lines.
E = hc/wavelength
E = 6.626E-34 x 3E8/420E-9 = ? J/photon.
E/photon = hc/wavelength
E/photon = approx 5E-19 J but you should confirm that for a more accurate answer.
32W = 32 J/s * 2s = 64 J
Then 5E-19 J/photon x # photons = 64 J.
Solve ofr # photons.