Use Balmer's formula to calculate (a) the wavelength, (b) the frequency, and (c) the photon ener

Use Balmer's formula to calculate (a) the wavelength, (b)...

Key Concepts

Balmer Series

The Balmer series refers to a set of spectral lines in the hydrogen atom that result from electron transitions from higher energy levels (n ? 3) down to the n = 2 level. This series is significant because many of its lines fall within the visible spectrum, and it played a key historical role in developing early atomic models and in the understanding of quantum transitions.

Balmer's Formula

Balmer's formula is an empirical relationship that provides the wavelengths of the hydrogen spectral lines in the Balmer series. In its form for hydrogen, it relates the inverse of the wavelength to the difference between the reciprocals of the squares of the lower and higher energy levels, typically using the Rydberg constant. This formula is essential for predicting the spectral lines and understanding the energy transitions in hydrogen.

Rydberg Constant

The Rydberg constant is a fundamental physical constant used in the calculation of atomic spectra, particularly in the expressions that describe the wavelengths of light emitted or absorbed by hydrogen. It appears in Balmer's formula and is critical for making accurate predictions of spectral line positions in various atomic transitions.

Frequency Calculation

The frequency of a photon is intrinsically linked to its wavelength through the speed of light in a vacuum. The relation c = ??, where c is the speed of light, ? is the wavelength, and ? is the frequency, allows one to calculate the frequency once the wavelength is determined. This calculation is foundational in connecting the quantum mechanical description of light with its classical wave properties.

Photon Energy Calculation

The energy of a photon can be calculated using Planck's relation, E = h?, which directly connects the energy of the photon to its frequency using Planck's constant. Alternatively, since frequency and wavelength are inversely related through the speed of light, the energy can also be expressed as E = hc/?. This relationship is fundamental in quantum physics for understanding the quantized nature of light and energy transitions in atoms.

Transcript

00:02 Okay, in this problem we're asked to look at the balmer, at a line in the balmer series, specifically that for the gamma line in hydrogen.

00:10 And for that particular line, we're asked to find the wavelength, frequency, and energy of the photon corresponding to this line.

00:17 So recall the equation, the bomber series, which gives us the wavelength in terms of this r value and a index for a lower and upper level, r is 1 .097, e.

00:31 The negative 7 inverse meters.

00:37 And recall, for the h gamma, the h gamma line, the lower value is n equals 2.

00:45 The upper value is n equals 5.

00:49 And the text discusses the convention for how these are determined.

00:53 The upper level increases with the greek letter.

00:58 So h alpha would be 3, beta, 4, gamma is 5.

01:04 That's how we get to these particular.

01:07 Indices.

01:10 So with that said, we can jump in, plug these values in, and find this lambda.

01:17 So as i mentioned, you just plug some numbers in.

01:23 So for the lower, we have one over the lower, 2 squared, minus one over the upper, 5 squared.

01:32 All this is inverse.

01:37 And after plugging these numbers in, plugging in our value for r computing, we are left with a value of 434 nanometers...

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