Question:
Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is :
Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is :
Updated On: Jul 9, 2024
- $ \frac{9}{31}$
- $ \frac{5}{27}$
- $ \frac{3}{23}$
- $ \frac{7}{29}$
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The Correct Option is B
Solution and Explanation
$\left(\frac{\lambda_{lyman}}{\lambda_{Balmer}}\right)_{max} -= \frac{\left(\frac{1}{2^{2}} - \frac{1}{3^{2}}\right)}{\left(\frac{1}{1^{2}} - \frac{1}{2^{2}}\right)} = \frac{5 / 36 }{3 / 4 } = \frac{5}{27}$
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Concepts Used:
Atomic Spectra
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an electron making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states.
Read More: Atomic Spectra
Spectral Series of Hydrogen Atom
Rydberg Formula:
The Rydberg formula is the mathematical formula to compute the wavelength of light.
\[\frac{1}{\lambda} = RZ^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})\]Where,
R is the Rydberg constant (1.09737*107 m-1)
Z is the atomic number
n is the upper energy level
n’ is the lower energy level
λ is the wavelength of light
Spectral series of single-electron atoms like hydrogen have Z = 1.
Uses of Atomic Spectroscopy:
- It is used for identifying the spectral lines of materials used in metallurgy.
- It is used in pharmaceutical industries to find the traces of materials used.
- It can be used to study multidimensional elements.