Use the Balmer equation to calculate the wavelength in nanometers of the spectral line for hydro

Use the Balmer equation to calculate the wavelength in...

Key Concepts

Unit Conversion for Photonic Energy

Unit conversion is an essential concept when dealing with photonic energy calculations. It involves converting energy values from joules (measured per photon) to kilojoules per mole by using Avogadro's number, ensuring that energy values are appropriately scaled for practical chemical and physical applications.

Energy-Wavelength Relationship

The energy-wavelength relationship is a key concept in quantum mechanics, described by Planck's equation (E = hc/?). This principle allows one to calculate the energy of a photon based on its wavelength, linking the wave and particle nature of light.

Rydberg Formula

The Rydberg formula is a mathematical expression that relates the wavelengths of the spectral lines of hydrogen and hydrogen-like elements to the quantum numbers of the electron transitions. It incorporates the Rydberg constant, which is a fundamental physical constant used to predict the wavelengths of these lines.

Balmer Series

The Balmer series comprises a set of spectral lines in the hydrogen atom that are produced when electrons transition from higher energy levels (n > 2) down to the n = 2 level. This series is important because it lies in the visible region of the electromagnetic spectrum, making it essential in studies of atomic physics and astrophysics.

Transcript

00:02 Okay, so for this question, we're going to use the rydberg equation, which is 1 over the wavelength, equals r, which is the rydberg constant, times 1 over m squared, minus 1 over n squared.

00:19 So when we talk about the balmer series, and quickly, this is also called the balmer equation too, or rydberg equation.

00:27 When we talk about the ballmer series, we talk about an electron dropping to m equals 2.

00:34 So we're going to set our m to 2, and then we're given that n equals 6.

00:39 So from there, we just need to solve for our wavelength.

00:43 So let's go ahead and plug in what we know.

00:45 We know that it's 1 over the wavelength equals r, which is 1 .0974 times 10 to the negative second.

00:57 I'm going to leave off my units just because i'm very slow with writing, but you should always write out your units.

01:04 And then we're going to say 1 over 2 squared minus 1 over 6 squared.

01:14 All right.

01:15 So if we go ahead and solve this, we are going to find that the wavelength equals 410 .2 nanometers.

01:28 All right.

01:29 So since we have the wavelength, we can now use this equation, e equals hc over the wavelength in order to find our energy.

01:42 And we know we want to in kilojoules per mole, so we know we're going to have to multiply this by avagadro's number to get it.

01:48 Ooh, that is a very big n.

01:50 Multiply it by avagadro's number to get it into moles.

01:55 Great.

01:56 So let's fill in what we know.

01:58 So we know h is plank's constant, which is six...

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