Math Problem Statement
. Calculate the wavelength, in nanometers, of the light emitted by a hydrogen atom when its electron transitions from the n = 8 to the n = 5 principal energy level. A. 3740 nm B. 984 nm C. 148 nm D. 24451 nm E. 1321 nm
Solution
To calculate the wavelength of light emitted during an electron transition in a hydrogen atom, we use the Rydberg formula:
Where:
- is the wavelength of the emitted light,
- is the Rydberg constant, ,
- is the initial energy level (in this case ),
- is the final energy level (in this case ).
Step 1: Calculate the wavelength
We can substitute the values into the equation:
Step 2: Simplify the expression
First, find a common denominator:
So, the equation becomes:
Step 3: Calculate the wavelength
Step 4: Convert to nanometers
Since :
Thus, the wavelength is 3740 nm, which corresponds to option A.
Answer: A. 3740 nm
Would you like further clarification or details?
Here are 5 related questions:
- How is the energy of a photon related to its wavelength?
- What is the significance of the Rydberg constant in quantum physics?
- How does the Bohr model of the hydrogen atom explain spectral lines?
- How do principal quantum numbers affect energy levels in an atom?
- What is the Balmer series, and how does it relate to visible hydrogen emissions?
Tip: When dealing with light transitions, higher energy differences result in shorter wavelengths, which corresponds to ultraviolet or visible light.
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Math Problem Analysis
Mathematical Concepts
Quantum Physics
Atomic Structure
Wavelength Calculation
Formulas
Rydberg formula: 1/λ = R_H (1/n_f^2 - 1/n_i^2)
Theorems
Rydberg's formula for hydrogen spectral lines
Suitable Grade Level
College Level (Introductory Physics or Chemistry)
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