Question:
The Bohr orbit radius for the hydrogen atom $(n=1)$ is approximately $0.530\,�$. The radius for the first excited state $(n=2)$ orbit is (in $�$ )
The Bohr orbit radius for the hydrogen atom $(n=1)$ is approximately $0.530\,�$. The radius for the first excited state $(n=2)$ orbit is (in $�$ )
Updated On: Jan 30, 2025
- 0.13
- 1.06
- 4.77
- 2.12
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The Correct Option is D
Solution and Explanation
Radius of hydrogen atom $=0.530\,�$,
Number of excited state $(n)=2$ and atomic number of hydrogen atom $(Z)=1$.
We know that the Bohr radius.
$(r)=\frac{n^{2}}{Z} \times=\frac{(2)^{2}}{1} \times 0.530$
$=4 \times 0.530=2.12\,�$
Number of excited state $(n)=2$ and atomic number of hydrogen atom $(Z)=1$.
We know that the Bohr radius.
$(r)=\frac{n^{2}}{Z} \times=\frac{(2)^{2}}{1} \times 0.530$
$=4 \times 0.530=2.12\,�$
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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.