Calculate The Wavelength Of The Light Emitted When An Electron In A Hydrogen Atom N=3 To N=1s – Calculate the Wavelength of Light Emitted When An Electron In A Hydrogen Atom N=3 To N=1s delves into the fascinating realm of atomic physics, where we explore the intricacies of light emitted during electron transitions. This journey begins with the Rydberg formula, a cornerstone in understanding the relationship between energy level transitions and the corresponding wavelengths of emitted light.
In this specific transition, we focus on the electron’s movement from the third energy level (n=3) to the ground state (n=1). Using the Rydberg formula, we calculate the energy difference between these levels, which is then converted into wavelength using the fundamental relationship E=hc/λ.
Understanding the Rydberg Formula
The Rydberg formula is a mathematical equation that calculates the wavelength of light emitted when an electron in an atom transitions from one energy level to another. It was developed by the Swedish physicist Johannes Rydberg in 1888.
The formula is given by:
1/λ = RH(1/n f2– 1/n i2)
where:
- λ is the wavelength of the emitted light
- R His the Rydberg constant, which is a fundamental constant of nature
- n fis the final energy level of the electron
- n iis the initial energy level of the electron
Calculating the Wavelength for the Specific Transition
To determine the wavelength of light emitted when an electron in a hydrogen atom transitions from n=3 to n=1, we need to follow these steps:
Identifying Initial and Final Energy Levels
The initial energy level is n=3, and the final energy level is n=1.
Calculating Energy Difference
Using the Rydberg formula, we can calculate the energy difference between these levels:
- E = -13.6 eV – (1/n f2– 1/n i2)
- E = -13.6 eV – (1/1 2– 1/3 2)
- E = -12.09 eV
Converting Energy Difference to Wavelength
Using the relationship E=hc/λ, we can convert the energy difference into wavelength:
- λ = hc/E
- λ = (6.626 x 10 -34J s) x (3 x 10 8m/s) / (-12.09 eV x 1.602 x 10 -19J/eV)
- λ = 102.6 nm
Therefore, the wavelength of light emitted when an electron in a hydrogen atom transitions from n=3 to n=1 is 102.6 nm.
Analyzing the Emitted Light
When an electron transitions from a higher energy level (n=3) to a lower energy level (n=1) in a hydrogen atom, it emits a photon of light. The characteristics of this emitted light are determined by the energy difference between the two energy levels.
Frequency of the Emitted Light
The frequency of the emitted light is directly proportional to the energy difference between the two energy levels. The higher the energy difference, the higher the frequency of the emitted light.
$E = hf$
where:
- $E$ is the energy of the emitted photon
- $h$ is Planck’s constant
- $f$ is the frequency of the emitted light
Wavelength of the Emitted Light
The wavelength of the emitted light is inversely proportional to the energy difference between the two energy levels. The higher the energy difference, the shorter the wavelength of the emitted light.
$E = hc/\lambda$
The wavelength of light emitted when an electron in a hydrogen atom transitions from n=3 to n=1 can be calculated using the Rydberg formula. The Rydberg constant is a fundamental constant that describes the energy levels of hydrogen atoms. Are jacky cheung and nick cheung brothers? This formula can be used to determine the wavelength of light emitted during atomic transitions in other elements as well.
where:
- $E$ is the energy of the emitted photon
- $h$ is Planck’s constant
- $c$ is the speed of light
- $\lambda$ is the wavelength of the emitted light
Color of the Emitted Light
The color of the emitted light is determined by its wavelength. Visible light has wavelengths ranging from 400 nm (violet) to 700 nm (red). The shorter the wavelength, the higher the energy of the emitted light, and the bluer the color.
Table of Key Parameters, Calculate The Wavelength Of The Light Emitted When An Electron In A Hydrogen Atom N=3 To N=1s
The following table summarizes the key parameters of the emitted light for the transition from n=3 to n=1 in a hydrogen atom:
| Parameter | Value |
|---|---|
| Frequency | 2.466 x 1015 Hz |
| Wavelength | 121.6 nm |
| Color | Ultraviolet |
Concluding Remarks: Calculate The Wavelength Of The Light Emitted When An Electron In A Hydrogen Atom N=3 To N=1s
In conclusion, the wavelength of light emitted during this transition corresponds precisely to the energy difference between the initial and final energy levels of the electron. This understanding not only provides insights into the behavior of electrons within atoms but also lays the foundation for various applications in spectroscopy and other fields of science.
Essential FAQs
What is the significance of the Rydberg formula?
The Rydberg formula provides a precise mathematical relationship between the wavelengths of light emitted during electron transitions and the energy levels involved.
How does the energy difference between atomic levels relate to the wavelength of emitted light?
The energy difference between atomic levels is inversely proportional to the wavelength of emitted light. Higher energy differences correspond to shorter wavelengths.
What are the practical applications of understanding electron transitions and emitted light wavelengths?
Understanding electron transitions and emitted light wavelengths has applications in various fields, including spectroscopy, astrophysics, and laser technology.
