The Bohr equation

The purpose of the Bohr equation is to give a ratio of physiological dead space volume to tidal volume. Dead space volume is normally around 30% of tidal volume and so the normal ratio is quoted as 0.3. Under abnormal conditions, the ratio will tend to increase and so make ventilation inefficient. 

Start with the theoretical lungs shown in the figure and remember that each Vt has a component that is dead space ( Vd) and a remainder that must take part in gas exchange at the alveolus (Vt - Vd). This is the alveolar volume. 

Now consider a single tidal exhalation. The C02 in this breath is equal to ft. Vt. This must be made up of alveolar gas (Fa [Vt - Vd]) and dead space gas (ft. Vd). 

The term Vd needs to be moved to the left, aiming for Vd/Vt in the final equation. Start by adding (Fa.I/d) to both sides and subtracting (Fe.I/t) from both sides to give 

To get I/d/I/t on the left, both sides must be divided by l/r. At the same time, the term Fa can be moved from left to right by also dividing both sides by Fa 

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State the first principles, for example the Bohr equation considers a single tidal exhalation comprising both dead space and alveolar gas. 

The physiological dead space can be calculated using the Bohr equation. 

Electromagnetic energy is quantized, where the amount of energy corresponding to 1 quantum of energy (or 1 photon), e, of a given frequency is described by the Bohr equation ... 

Explain this trend on the basis of the Bohr equation for energy levels of single-electron systems. 

Fig. 5.21 shows a liquid jet ejected from a cylindrical capillary of diameter 2r. Prior to break-up into individual drops, the liquid jet surface oscillates with wavelength X and amplitude Ar = r - r . The surface tension can be calculated from the wave parameters of two adjacent nodes using the Bohr equation. 

During the 19th century, a number of experimental observations were made which were not consistent with the classical view that matter could interact with energy in a continuous form. Work by Einstein, Planck and Bohr indicated that in many ways electromagnetic radiation could be regarded as a stream of particles (or quanta), for which the energy, E, is given by the Bohr equation, as follows ... 

When applied to the hydrogen atom, Bohr s theory worked well however, the theory failed when atoms with two or more electrons were considered. Modifications such as elliptical rather than circular orbits were unsuccessfully introduced in attempts to fit the data to Bohr s theory. The developing experimental science of atomic spectroscopy provided extensive data for testing Bohr s theory and its modifications. In spite of the efforts to fix the Bohr theory, the theory ultimately proved unsatisfactory the energy levels predicted by the Bohr equation above and shown in Figure 2.2 are valid only for the hydrogen atom and... 

Measurement of physiologic dead space is based on the assumption that there is almost complete equilibrium between alveolar PCO2 and pulmonary capillary blood. Therefore, the arterial pCOj represents mean alveolar PCO2 over many breaths when an arterial blood sample is drawn for analysis of PCO2. The Bohr equation for physiologic dead space is... 

Bohr interpreted spectral lines in the hydrogen spectrum in terms of electronic transitions within the hydrogen atom. The Bohr equation (1.15) expresses the idea that Ej - E, represents the difference in energy between the two levels, A , and may be written in the form ... 

This has the same type denominator as the Bahner formula and when the other numbers are compared, it is found that the Bohr equation is essentially the same as the Balmer equation. There is only a slight difference due to the fact that the nucleus in the Bohr model is fixed at die center of the atom while the real spectra include the fact that the electron and proton both orbit around the center-of-mass (the see-saw balance point) of the two particles. That is really very close to the position of the proton because it is much more massive than the electron. When this correction is made to the Bohr formula, the agreement with the experimental spectra is essentially exact. 

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