Home/Class 12/Physics/

Question and Answer

Using the Rydberg formula. calculate the wavelengths of the first four spectral lines in the Lyman series of the hydrogen spectrum.
loading
settings
Speed
00:00
03:02
fullscreen
Using the Rydberg formula. calculate the wavelengths of the first four spectral lines in the Lyman series of the hydrogen spectrum.

Answer

The Rydberg formula is
\(\mathit{hc}\text /\lambda _{\mathit{ij}}=\dfrac{me^4}{8\varepsilon _o^2h^2}\left(\dfrac 1{n_f^2}-\dfrac 1{n_i^2}\right)\)
The wavelengths of the first four lines in the Lyman series correspond to transitions from \(n_i=2.3.4.5\)  to \(n_f=1.\)  We know that \(\dfrac{me^4}{8\varepsilon _0^2h^2}=13.6\;\mathit{eV}=21.76\times 10^{-19}J\)
Therefore.
\(\lambda _{11}=\dfrac{\mathit{hc}}{21.76\times 10^{-19}\left(\dfrac 1 1-\dfrac 1{n_1^2}\right)}m\)
\(=\dfrac{6.625\times 10^{-34}\times 3\times 10^8\times n_1^2}{21.76\times 10^{-19}\times (n_i^2-1)}m=\dfrac{0.9134n_i^2}{(n_i^2-1)}\times 10^{-7}m\)
\(=913.4\;n_t^2/(n_t^2-1)\;Å\)
Substituting \(n_4=2.3,4.5.\)  we get
\(\lambda _{21}=1218\;Å \)   \(.\lambda _{31}=1028\text{A.}\lambda _{41}=974.3\;A\)  and \(\lambda _{51}=951.4\;Å \)  
To Keep Reading This Answer, Download the App
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
To Keep Reading This Answer, Download the App
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
Correct7
Incorrect0
Watch More Related Solutions
Consider the statements \(S_{1}\) and \(S_{2}\) :
\(S_{1}:\) Conductivity always increases with decrease in the concentration of electrolyte.
\(S_{2}:\) Molar conductivity always increases with decrease in the concentration of electrolyte.
The correct option among the following is( )
A. \(S_{1}\) is correct and \(S_{2}\) is wrong
B. \(S_{1}\) is wrong and \(S_{2}\) is correct
C. Both \(S_{1}\) and \(S_{2}\) are wrong
D. Both \(S_{1}\) and \(S_{2}\) are correct
Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is \(6\sqrt {3}r.\)
Pick an appropriate option to justify the given statement:
Size of an atom in Rutherford’s model is _________ the size of an atom compared to Thomson’s model. \((\)Less than, Greater than, no different than\()\)
Rubber tyres are preferred over steel tyres. Why?
A cricket ball is thrown at 'a speed of \(28\ ms^{-1}\) in a direction \(30^{\circ }\) above the horizontal. Calculate the maximum height, the time taken by the ball to return to the same level and the horizontal distance from the point of protection to the point where the ball returns to the level.
You may have seen in a circus a motorcyclist driving in a vertical loops inside a death-well (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is \(25 \;m\) ?
If the sum of length of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is \(\frac {\pi }{3}\)
Why does friction decrease on lubrication?
\((A)\) follows first order reaction\(, (A)\to \) product. Concentration of \(A,\) changes from \(0.1M\) to \(0.025M\) in \(40\) min. Find the rate of reaction of \(A\) when concentration of \(A\) is \(0.01M\)( )
A. \(3.46\times 10^{-4}M\ min^{1}\)
B. \(3.47\times 10^{-5}M\ min^{-1}\)
C. \(1.73\times 10^{-4}M\ min^{-1}\)
D. \(1.73\times 10^{-5}M\ min^{-1}\)
Pick an appropriate option to justify the given statement:
Even in the case of stable equilibrium _________ electrons experience a net force, though _______ electrons do not. \(\text{[Rutherford's model, Thomson's model]}\)

Load More