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The Balmer Series Essay

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Physics
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The Balmer series
Abstract
This experiment aims to study the hydrogen spectrum and compare the observation to
the Balmer’s formula. The mercury source was used to test for the accuracy of the apparatus
and was then replaced with the hydrogen source. The wavelengths of the spectral lines were
observed and recorded. A graph of the reciprocal of the wavelength versus the reciprocal of
the square of the quantum numbers was drawn. From the calculations, the Rydberg constant
was calculated to be 1.20956 

. This value was in agreement with the theatrical
value. However, there was an error of a 10.22% difference from the theoretical value. The
errors in observing the data may have contributed to this.
Introduction
The Balmer series is named after the Swiss teacher Johann Balmer who noted that
hydrogen atom in a discharge lamp emits a series of select wavelengths of the visible light
spectrum. The Balmer formula was later generalized into Rydberg formula
,
where
is the Rydberg constant for hydrogen 1.097 


,
is the initial quantum
number. At the same time,
is the final quantum number (Beyer et al. 2017). For the
Balmer series, the
is equal to 2.

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From the Bohr model of the atom, bound electrons only have discrete energy levels.
An electron emits energy when it falls from an excited state to a lower state. The energy is
released in quantized amounts called quanta. The energy of the photon is expressed as
follows 

. Where the frequency of light is, is the wavelength,  is the quanta
of energy, and h is the Planck's constant equals to 

While c is the speed of
light. The light emitted from a hydrogen atom has a wavelength that is related to the energy
and color. Other series that exist include Brackett series with
, Lyman Series
,
and Paschen Series
(Lincoln, 2019).
Balmer series is significant and is used in astronomy since the Balmer lines are
detected in numerous stellar objects as a result of the abundance of hydrogen in the universe
(Ortiz-Mora et al. 2020). The hydrogen spectrum is significant as all observed spectral lines
are as a result of electrons moving between the energy levels in atoms. This spectral series is
applied in astronomy for detecting the hydrogen as well as calculating redshifts.
Procedure
The apparatus used in the experiment include hydrogen discharge tube, mercury
discharge tube, incandescent lamp, and spectrometer with the diffraction grating.
Using the spectroscope, the eye was positioned at the eyepiece while pointing the
line-up slot at the incandescent light source. While holding the spectroscope firm and without
moving the head, the spectral lines on the scale were observed. The range of wavelengths in
nanometres (nm) and colors was observed on the spectroscope and recorded. Mercury source
was also analyzed using the spectrometer, and the line spectral were recorded, including color

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1 The Balmer series Abstract This experiment aims to study the hydrogen spectrum and compare the observation to the Balmer’s formula. The mercury source was used to test for the accuracy of the apparatus and was then replaced with the hydrogen source. The wavelengths of the spectral lines were observed and recorded. A graph of the reciprocal of the wavelength versus the reciprocal of the square of the quantum numbers was drawn. From the calculations, the Rydberg constant was calculated to be 1.20956× 107 𝑚−1 . This value was in agreement with the theatrical value. However, there was an error of a 10.22% difference from the theoretical value. The errors in observing the data may have contributed to this. Introduction The Balmer series is named after the Swiss teacher Johann Balmer who noted that hydrogen atom in a discharge lamp emits a series of select wavelengths of the visible light 1 1 1 spectrum. The Balmer formula was later generalized into Rydberg formula 𝜆 = 𝑅𝐻 (𝑛2 − 𝑛2 ), 𝑓 𝑖 where 𝑅𝐻 is the Rydberg constant for hydrogen 1.097× 10−7 𝑚−1, 𝑛𝑖 is the initial quantum number. At the same time, 𝑛𝑓 is the final quantum number (Beyer et al. 2017). For the Balmer series, the 𝑛𝑓 is equal to 2. 2 From the Bohr model of the atom, bound electrons only have discrete energy levels. An electron emits energy when it falls from an excited state to a lower state. The energy is released in quantized amounts called ...
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