“It doesn't matter how beautiful your theory is ... If it doesn't agree with the experiment, it's wrong".
According to the standard cosmology, nearby
and distant galaxies {1} recede from the Earth because the Universe is expanding at a constant rate.
This theory states that the wavelength of light
coming from these galaxies increases or shows cosmological redshift. If this
shift is denoted as z can be defined by the following
equation
1 + z = λE/λG … (1)
where λG is the wavelength of
light emitted by a galaxy (or any astronomical object) and λE is the wavelength of this light measured by an
Earth’s observer.
Bohr’s equation for energy levels of the
hydrogen (H) atom is
En= 1/n2(−2π2e4m/h2)… (2)
where n (= 1, 2, 3,) is the quantum number, m is the mass of the electron, e (= 1.6×10-19 C) is its charge and h (= 6.63×10-34 J sec) is Planck’s constant.[1]
The spectrum of H atoms is dominated by a series of lines, the highest in energy being the Lyman series from 121.6 nm - 92.1 nm in the far-ultraviolet (UV) region. The hydrogen (Lyman) alpha-line or Ly-α at 121.6 nm is of utmost importance in many fields of astrophysics. For the sake of simplicity, we will mainly deal in this communication with the Ly-α line.
The energy of the photon emitted by the H atom during its transition from the higher (excited) energy level with n = 2 to the ground level with n = 1 is
hν = 3/2(π2e4m/h2)
where ν is the frequency of the emitted photon. This is the equation for the energy of the Ly-α line: 10.2 eV. This energy is more than enough to ionize all alkali metals whose first ionization potential ranges between 3.89 eV (cesium) to 5.39 eV (lithium).
EGSY8p7 is a distant galaxy, with a spectroscopic redshift of z = 8.68 [Wikipedia EGSY8p7]. EGSY8p7 is the most distant known detection of the Lyα emissions. This detection is surprising because the early Universe was full of atomic H clouds which should absorb these emissions.
We know that the frequency equals the speed of light divided by the wavelength. Multiplying the reciprocal of eqn. (1) with c/h and after a bit of algebra we arrive at
hνE = hνG/(1 + z) = 10.2 eV/9.68 = 1.05 eV
where hνG is the energy of light emitted by EGSY8p7 and hνE is the energy of this light received by the Earth’s observer and νG and νE are the corresponding frequencies. The received energy is far less than the first ionization potential of alkali metals and, therefore, it will not be able to ionize them. Moreover, this energy is by a factor (1 + z) lower than the energy of the light emitted by EGSY8p7. This is in violation of the Principle of energy conservation which is one of the basic laws of physics. As far as we are aware, no violation of this law has ever been experimentally observed.
If we adopt the conservation law then
hνG = hνE = hν
or
νG = νE = ν.
As we noted above, the frequency equals the speed of light divided by the wavelength then combining this equation and eqn. (1) we find that
cG = c/(1 + z)
where cG is the speed of light emitted by a galaxy (or any astronomical object) and c (= 299792 km sec-1) is the (current) speed of this light observed by an Earth’s observer. In other words, the speed of light emitted by EGSY8p7, cG, is lower for a factor (1 + z) than the speed of this light received by the Earth’s observer or the current speed of light c.
References
[1] We define nearby galaxies as those galaxies whose redshift z is from 0.001 to 0.1 (or 0.001 ≤ z ≤ 0.1) and distant galaxies those having z > 0.1 [1, 2]. Of course, there is no sharp boundary between nearby and distant galaxies.
[2] It is often considered that the Schrödinger equation is superior to Bohr’s equation in describing the H
atom. In most cases, the results of both approaches coincide or are very close.
.jpg)
No comments:
Post a Comment