Advertisements
Advertisements
Question
Determine the series limit of Balmer, Paschen, and Pfund series, given the limit for Lyman series is 912 Å.
Advertisements
Solution
Data: `lambda_("L"∞)` = 912 Å
For hydrogen spectrum, `1/lambda = "R"_"H"(1/"n"^2 - 1/"m"^2)`
∴ `1/lambda_("L"∞) = "R"_"H"(1/1^2 - 1/∞) = "R"_"H"` ...(1)
as n = 1 and m = ∞
`1/lambda_("B"∞) = "R"_"H"(1/4 - 1/∞) = "R"_"H"/4` .....(2)
as n = 2 and m = ∞
`1/lambda_("Pa"∞) = "R"_"H"(1/9 - 1/∞) = "R"_"H"/9` .....(3)
as n = 3 and m = ∞
`1/lambda_("Pf"∞) = "R"_"H"(1/25 - 1/∞) = "R"_"H"/25` ......(4)
as n = 5 and m = ∞
From Eqs. (1) and (2), we get,
`lambda_("B"∞)/lambda_("L"∞) = "R"_"H"/("R"_"H"//4) = 4`
∴ `lambda_("B"∞) = 4 lambda_("L"∞) = (4)(912)` = 3648 Å
This is the series limit of the Balmer series.
rom Eqs. (1) and (3), we get,
`lambda_("Pa"∞)/lambda_("L"∞) = "R"_"H"/("R"_"H"//9)` = 9
∴ `lambda_("Pa"∞) = 9lambda_("L"∞) = (9)(912)` = 8208 Å
This is the series limit of the Paschen series.
From Eqs. (1) and (4), we get,
`lambda_("Pf"∞)/lambda_("L"∞) = "R"_"H"/("R"_"H"//25)` = 25
∴ `lambda_("Pf"∞) = 25 lambda_("L"∞) = (25)(912)` = 22800 Å
APPEARS IN
RELATED QUESTIONS
An electron jumps from fourth to first orbit in an atom. How many maximum number of spectral lines can be emitted by the atom? To which series these lines correspond?
In both β− and β+ decay processes, the mass number of a nucleus remains the same, whereas the atomic number Z increases by one in β− decay and decreases by one in β+ decay. Explain giving reason.
Which of the following transition will have highest emission wavelength?
If wavelength for a wave is `lambda = 6000 Å,` then wave number will be ____________.
Let v1 and v3 be the frequency for series limit of Balmer and Paschen series respectively. If the frequency of first line of Balmer series is v2 then, relation between v1 and v2 and v3 is ____________.
In hydrogen spectrum, which of the following spectral series lies in ultraviolet region?
In hydrogen spectrum, the series of lines obtained in the ultraviolet region of the spectrum is ____________.
If the mass of the electron is reduced to half, the Rydberg constant ______.
Each element is associated with a ______.
Continuous spectrum is produced by ______.
To produce an emission spectrum of hydrogen it needs to be ______.
What is the minimum energy that must be given to a H atom in ground state so that it can emit an Hγ line in Balmer series. If the angular momentum of the system is conserved, what would be the angular momentum of such Hγ photon?
Deutrium was discovered in 1932 by Harold Urey by measuring the small change in wavelength for a particular transition in 1H and 2H. This is because, the wavelength of transition depend to a certain extent on the nuclear mass. If nuclear motion is taken into account then the electrons and nucleus revolve around their common centre of mass. Such a system is equivalent to a single particle with a reduced mass µ, revolving around the nucleus at a distance equal to the electron-nucleus separation. Here µ = meM/(me + M) where M is the nuclear mass and m e is the electronic mass. Estimate the percentage difference in wavelength for the 1st line of the Lyman series in 1H and 2H. (Mass of 1H nucleus is 1.6725 × 10–27 kg, Mass of 2H nucleus is 3.3374 × 10–27 kg, Mass of electron = 9.109 × 10–31 kg.)
Determine the shortest wavelengths of Balmer and Pasch en series. Given the limit for the Lyman series is 912 Å.
The frequencies for series limit of Balmer and Paschen series respectively are 'v1' and 'v3'. If frequency of first line of Balmer series is 'v2' then the relation between 'v1', 'v2' and 'v3' is ______.
In the hydrogen atoms, the transition from the state n = 6 to n = 1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition.
The frequency of the series limit of the Balmer series of the hydrogen atoms of Rydberg’s constant R and velocity of light c is ______.
What condition of an atomic gas or vapour produces an emission line spectrum?
How does radiation from an excited atomic gas or vapour appear when analysed with a spectroscope?
The hydrogen spectrum is an example of which type of spectrum?
What type of spectrum is produced when white light passes through an atomic gas or vapour and dark lines appear?
What is passed through an atomic gas or vapour to produce an absorption spectrum?
Why can line spectra be used as fingerprints to identify gases?
How do the wavelengths of dark lines in an absorption spectrum relate to the bright lines in the emission spectrum of the same gas?
