többszintű címsorok：Determine Likewise the Wavelength of the Third Lyman Line
Bevezetés
The Lyman series is a series of lines in the ultraviolet (UV) region of the electromagnetic spectrum that are emitted by excited hydrogen atoms. These lines are named after Theodore Lyman, who first observed them in the early 1900s. Each line corresponds to a transition of an electron from a higher energy level to the first energy level (n=1) in hydrogen.
Explanation of Lyman Series
The Lyman series is characterized by a series of transitions where the electron jumps from higher energy levels (n>1) down to the first energy level (n=1). The energy of each transition determines the wavelength of the emitted electromagnetic radiation. The Lyman series covers a range of wavelengths from the UV to the X-ray region.
Determining the Wavelength of the Third Lyman Line
To determine the wavelength of the third Lyman line, we need to understand the relationship between the energy levels and the corresponding wavelengths. The energy levels in hydrogen are given by the formula:
E = -13.6 eV/n2
where E is the energy in electron volts (eV) and n is the principal quantum number.
For the Lyman series, the initial energy level (n?) is always higher than the final energy level (n?=1). The energy difference between the two levels is given by:
ΔE = E(n?) – E(n?)
For the third Lyman line, the initial energy level is n?=4. Plugging this value into the energy formula, we can calculate the energy of the transition:
E(n?=4) = -13.6 eV/42 = -3.4 eV
Now, we need to convert this energy into wavelength using the formula:
E = hc/λ
where h is Planck’s constant (6.626 x 10?3? J?s) and c is the speed of light (3.00 x 10? m/s). Converting eV to joules using the conversion factor 1 eV = 1.602 x 10?1? J, we get:
-3.4 eV = -3.4 x 1.602 x 10?1? J
Plugging in these values, we can solve for the wavelength:
-3.4 x 1.602 x 10?1? J = (6.626 x 10?3? J?s)(3.00 x 10? m/s)/λ
Simplifying the equation, we find:
λ = (6.626 x 10?3? J?s)(3.00 x 10? m/s) / (-3.4 x 1.602 x 10?1? J)
Calculating this equation yields the wavelength of the third Lyman line.
Következtetés
The Lyman series is an important spectral series that provides insights into the atomic structure of hydrogen atoms. By understanding the relationship between energy levels and wavelengths, we can determine the wavelength of specific lines in the Lyman series. In the case of the third Lyman line, we have calculated its wavelength by using the energy formula and converting the energy into wavelength using Planck’s constant and the speed of light.
