We appreciate your visit to When an electron jumps between the following shells the wavelengths of the radiations emitted are From the 2nd to the 1st shell tex lambda 1. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The wavelength relationship for electron transitions in a hydrogen atom is λ₃ < λ₁ < λ₂, with λ₃ being the shortest wavelength for the 3rd to 1st transition and λ₂ the longest for the 3rd to 2nd transition.
To understand the relationship between these wavelengths, we need to delve into the Bohr model of the atom and the concept of energy levels in hydrogen atoms. According to the Bohr model:
- The energy of an electron in the nth orbit of a hydrogen atom is given by: Eₙ = -13.6 eV/n²
- The wavelength (λ) of the emitted photon when an electron transitions from a higher energy level (n₂) to a lower one (n₁) can be found using the Rydberg formula: 1/λ = R(1/n₁² - 1/n₂²) where R is the Rydberg constant (1.097 × 10⁷ m⁻¹)
Given the transitions:
- For the transition from the 2nd to 1st shell (n₂=2 to n₁=1): 1/λ₁ = R(1/1² - 1/2²) = R(1 - 1/4) = 3R/4
- For the transition from the 3rd to 2nd shell (n₂=3 to n₁=2): 1/λ₂ = R(1/2² - 1/3²) = R(1/4 - 1/9) = 5R/36
- For the transition from the 3rd to 1st shell (n₂=3 to n₁=1): 1/λ₃ = R(1/1² - 1/3²) = R(1 - 1/9) = 8R/9
From these equations, we can see the relationship:
- λ₃ < λ₁ < λ₂ since 8R/9 > 3R/4 > 5R/36.
This demonstrates that the wavelength of radiation emitted is inversely proportional to the energy difference between the two levels.
Complete Question:
When an electron jumps from 2nd to 1st, 3rd to 2nd, and 3rd to 1st shells, the wavelength of radiations emitted is λ₁, λ₂, λ₃, respectively. The relationship between wavelengths is?
Thanks for taking the time to read When an electron jumps between the following shells the wavelengths of the radiations emitted are From the 2nd to the 1st shell tex lambda 1. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
