Answer
Verified
452.7k+ views
Hint: Try to use the Rydberg formula and derive the Balmer formula from there. There I have an equation that relates Rydberg constant, wavelength and the number of orbits the electron jumps into.
Complete step-by step answer:
In order to answer our question, we need to know about the line spectrum. The hydrogen spectrum is an example of line emission spectrum. The line spectrum of hydrogen is obtained by passing an electric discharge through hydrogen as at low pressure. Hydrogen molecules split up into atoms. These electrons absorb energy and electrons get discharged. When these excited electrons come back to ground state they emit electromagnetic radiation of discrete frequencies. Now, when these emitted radiations are passed through prism then discontinuous line spectrum of several isolated sharp lines is observed. This is how the line spectrum of hydrogen looks like:
Now, the relation between wavelength and the number of spectral lines is: $\dfrac{1}{\lambda }=R{{z}^{2}}(\dfrac{1}{{{n}_{1}}^{2}}-\dfrac{1}{{{n}_{2}}^{2}})$, where R= Rydbergs constant z=atomic number(1 in this case). When ${{n}_{1}}=2$, then the series of lines which are obtained by the above formula are called the Balmer series. The hydrogen spectrum consists of several series of spectral lines named after their discoverer. These series are Lyman series, Balmer series, Paschen series, Brackett series and Pfund series. The value $1.09\times {{10}^{7}}$ is called the Rydberg’s constant for the hydrogen atom. Now, let us find our answer by putting the values in the Balmer formula. So, we have:
$\dfrac{1}{\lambda }=1.09\times {{10}^{7}}(\dfrac{1}{{{2}^{2}}}-\dfrac{1}{{{3}^{2}}})=1.09\times {{10}^{7}}(\dfrac{1}{4}-\dfrac{1}{9})=1.09\times {{10}^{7}}(\dfrac{5}{36})$
So, we obtain
$\begin{align}
& \dfrac{1}{\lambda }=1.52\times {{10}^{6}} \\
& So,\,\,\lambda =0.64\times {{10}^{-6}}m \\
\end{align}$
So, the wavelength of the Balmer series for n=3 is $0.64\times {{10}^{-6}}m$.
NOTE: The following table shows the relation between the names of series, their ‘n’ values and their spectral region:
Complete step-by step answer:
In order to answer our question, we need to know about the line spectrum. The hydrogen spectrum is an example of line emission spectrum. The line spectrum of hydrogen is obtained by passing an electric discharge through hydrogen as at low pressure. Hydrogen molecules split up into atoms. These electrons absorb energy and electrons get discharged. When these excited electrons come back to ground state they emit electromagnetic radiation of discrete frequencies. Now, when these emitted radiations are passed through prism then discontinuous line spectrum of several isolated sharp lines is observed. This is how the line spectrum of hydrogen looks like:
Now, the relation between wavelength and the number of spectral lines is: $\dfrac{1}{\lambda }=R{{z}^{2}}(\dfrac{1}{{{n}_{1}}^{2}}-\dfrac{1}{{{n}_{2}}^{2}})$, where R= Rydbergs constant z=atomic number(1 in this case). When ${{n}_{1}}=2$, then the series of lines which are obtained by the above formula are called the Balmer series. The hydrogen spectrum consists of several series of spectral lines named after their discoverer. These series are Lyman series, Balmer series, Paschen series, Brackett series and Pfund series. The value $1.09\times {{10}^{7}}$ is called the Rydberg’s constant for the hydrogen atom. Now, let us find our answer by putting the values in the Balmer formula. So, we have:
$\dfrac{1}{\lambda }=1.09\times {{10}^{7}}(\dfrac{1}{{{2}^{2}}}-\dfrac{1}{{{3}^{2}}})=1.09\times {{10}^{7}}(\dfrac{1}{4}-\dfrac{1}{9})=1.09\times {{10}^{7}}(\dfrac{5}{36})$
So, we obtain
$\begin{align}
& \dfrac{1}{\lambda }=1.52\times {{10}^{6}} \\
& So,\,\,\lambda =0.64\times {{10}^{-6}}m \\
\end{align}$
So, the wavelength of the Balmer series for n=3 is $0.64\times {{10}^{-6}}m$.
NOTE: The following table shows the relation between the names of series, their ‘n’ values and their spectral region:
Series | ${{n}_{1}}$ | ${{n}_{2}}$ | Spectral Region |
Lyman | 1 | 2,3,.. | Ultraviolet |
Balmer | 2 | 3,4,.. | Visible |
Paschen | 3 | 4,5,… | Infrared |
Brackett | 4 | 5,6,… | Infrared |
Pfund | 5 | 6,7,…. | Infrared |
Recently Updated Pages
Identify the feminine gender noun from the given sentence class 10 english CBSE
Your club organized a blood donation camp in your city class 10 english CBSE
Choose the correct meaning of the idiomphrase from class 10 english CBSE
Identify the neuter gender noun from the given sentence class 10 english CBSE
Choose the word which best expresses the meaning of class 10 english CBSE
Choose the word which is closest to the opposite in class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Why is there a time difference of about 5 hours between class 10 social science CBSE
Distinguish between Conventional and nonconventional class 9 social science CBSE