Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm) b. visible light (500 nm) c. ultraviolet radiation (150 nm)

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Welcome back everyone. We need to calculate the energy and kill a jewels of 2.50 moles of photons for radiation with a wavelength of 2 95 nanometers within the UV region. We're going to begin by recalling that we can utilize our plank Einstein equation in which our energy change of a photon is related to Planck's constant, multiplied by the speed of light, divided by lambda. Where we recall that lambda represents our wavelength. Recognize that lambda is going to be expressed in units of meters in this equation and our energy change of a photon is expressed in units of joules per photon. Now we need to recognize that the given wavelength from the prompt is in nanometers. So we're going to have to convert our lambda equal to 2 95 nanometers and multiplied by the conversion factor to go from nanometers. In the denominator two m in the numerator, we would recall that our prefix nano tells us that we have 10 to the negative ninth power of our base unit meter. So canceling out nanometers were left with meters and this is going to result in a wavelength equal to a value of 2.95 times 10 to the negative seven power meters. Now going to our formula to solve for delta E, plugging in first plank's constant represented by H. We recall that it's a value of 6.626 times 10 to the negative 34th power jewels times seconds. Then plug in our speed of light. We have a value of three point oh times 10 to the eighth Power units of meters per second. And then in our denominator we would plug in our wavelength, which we just converted to meters as 2.95 times 10 to the negative seven power meters. So now canceling out our units, recognize that we can get rid of meters with meters in the numerator seconds with our inverse seconds and we're left with jewels which we will interpret as jewels per photon for our energy change of a photon. And so simplifying this question in our calculators will come up with a value in which we don't want to round up at all. We want to include as many decimal places as possible. So we should have a value of 6. times 10 to the negative 19th power. And as we said, we're interpreting this energy as jewels per photon. Now going back to the prompt, we're told to calculate the energy and kill a jewels of 2.5 moles of photons. So we're going to need to multiply by a conversion factor to go from Jules per photon to kill jules per mole of photons. And so our first conversion factor that will multiply two is going to be going from jewels to kill a jewels by recalling that our prefix kilo tells us that we have an equivalent of 10 to the third power of our base unit jewels. So canceling out jewels, we have killed jules per photon but we need to introduce moles. So we're going to multiply by our conversion factor where we can compare quantities using avocados number where we can recall that we have six point oh times 10 to the 23rd power photons equivalent to one mole of photons. This allows us to cancel out photons in the denominator here with photons in the numerator, leaving us with killer joules per mole of photons as our final unit. And this is going to simplify to a value of 4.05 or sorry, .780732, 2 units of kila jewels per mole of photons. And now we can finally get to our final answer in which we're going to multiply this energy per mole of photons by are given 2.50 mol of photons. And so we have 405. being in units of kilograms per mole of photons In which we want to multiply by our unit 2. moles of photons. And so we can cancel out moles of photons leaving us with killer jewels as our final unit for energy. And this is going to result in a value equal to 1. times 10 to the third power modules. And this is going to represent our energy and 2.5 moles of photons corresponding to choice be in the multiple choice as our final answer. So I hope this was helpful and let us know if you have any questions.

Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm) b. visible light (500 nm) c. ultraviolet radiation (150 nm)

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Key Concepts

Photon Energy

Wavelength and Frequency

Moles and Avogadro's Number