What is the energy of each of the following photons in...

What is the energy of each of the following photons in kilojoules per mole?
(a) $\nu=5.97 \times 10^{19} \mathrm{~s}^{-1}$
(b) $\nu=1.26 \times 10^{6} \mathrm{~s}^{-1}$
(c) $\lambda=2.57 \times 10^{2} \mathrm{~m}$

Key Concepts

Unit Conversion and Avogadro's Number

This concept involves converting the energy of a single photon, typically calculated in joules, into energy per mole, usually expressed in kilojoules per mole. This is achieved by multiplying the energy per photon by Avogadro's number, which is the number of particles in one mole, and converting the resulting value from joules to kilojoules. This conversion bridges the microscopic and macroscopic scales in chemistry and physics.

Relationship Between Frequency and Wavelength

This concept describes the intrinsic link between a photon's frequency and its wavelength through the speed of light, given by the equation c = ??. It is crucial for converting between wavelength and frequency, which is especially important when the energy must be computed from different types of electromagnetic radiation information.

Photon Energy Equation

This concept involves calculating the energy of a photon using the quantum relation E = h? when the frequency is known or E = hc/? when the wavelength is provided. It is fundamental in quantum mechanics and signifies the quantization of energy, where h is Planck's constant and c is the speed of light.

Transcript

00:01 In this problem, we're asked to calculate the energy for three different scenarios.

00:07 We're asked to calculate the energy in kilojoules per mole.

00:12 Our first problem is a frequency of 5 .97 times 10 to the 19th hertz or s to the minus 1.

00:25 To calculate energy for this one, it's super easy, but we do have to get it to the right units.

00:30 We're just going to use energy equals plunks constant times our new so we're going to take planx constant which is 6 .626 times 10 to the negative 34th joules seconds times 5 .97 times 10 to the 19th seconds to the minus 1 and that will give me an energy in jewels of 3 .9557 times 10 to the minus 14th joules per photon and then and then we want to convert this to kilojoules per mole, so i'm going to multiply that by avogadro's number, which of course is 6 .022 times 10 to the 23rd photons per mole.

01:49 And then let's just go ahead and convert our joules to kilojoules like this.

01:57 And my first answer will be 2 .382, and i'm going to report this to three significant figures, 2 .38 times 10 to the seventh.

02:14 And i put my units down here, kilojoules per mole.

02:19 Problem one.

02:22 Problem two will also be this easy because we're also given hertz.

02:29 I guess it's b.

02:30 So i'm just going to go ahead and write e equals plunk's constant.

02:42 I'm writing too big here.

02:46 Times our given, which is 1 .26, times 10 to the 6th, s to the minus 1.

03:02 That equals 8 .349 times 10 to the negative 28th joules per photon.

03:17 And then again we're going to repeat this step.

03:34 First avagadro's number.