(b) What is the energy of one of these photons?

Question

Accepted Answer

Hey everyone in this example we have a ray of ultraviolet light with the given wavelength 321 nanometers. We need to calculate the energy for one mole of photons of this light. So we should recall that our formula for energy is that it's going to equal plank's constant, multiplied by our speed of light divided by our wavelength. Recognize that our wavelength is given in units of meters, sorry, in units of nanometers. And we should convert this two units of meters. So we're going to first find our energy by in our numerator, taking plank's constant, which we recall is 6.626 times 10 to the negative 34th power jewels, time seconds. And then plugging in our speed of light, which we recall is 3.00 times 10 to the positive eighth power and units of meters per second in our denominator. We want to go ahead and Plug in our given wavelength given as 321 nm. Which we will want to cancel out our units of nanometers by placing them in the denominator and then placing our final unit meters in the numerator. And we should recall that our prefix nano tells us. We have 10 to the negative ninth power meters. So now we're able to cancel our units of nanometers. We're left with meters but we can go ahead and cancel our meters because we have them in the numerator as well. And then we can go ahead and cancel out those inverse seconds in the numerator with the other seconds from our plank's constant. And this leaves us with jewels as our final unit of energy here. What this will give us is a value equal to 6.19 times 10 to the negative 19th power and our units are jewels per photon. However, we want our units to be in and in units of jewels per mole Of our photons. And so we're going to use the conversion factor where we're going to take this energy 6.19 times 10 to the negative 19th powered jewels per photon. And we want to cancel out that photon unit there. So we're going to go ahead and recall that we should have 6.022 times 10 to the 23rd power photons which is avocados number permanent. And so this is going to allow us to go ahead and cancel our units of photons, leaving us with jewels per mole as our final unit. And what we're going to get here is a value equal to 370, 762 which we can go ahead and convert to scientific notation as 3.73 times 10 to the Positive 5th power and units of jewels per mole. Or we can say for one mole of photons. And so this would be our final answer to complete this example. So I hope that everything I reviewed was clear. But if you have any questions, please leave them down below and I will see everyone in the next practice video.

(b) What is the energy of one of these photons?

Verified Solution

Key Concepts

Photon Energy

Planck's Constant

Electromagnetic Spectrum