Advertisements
Advertisements
Question
Determine the series limit of Balmer, Paschen and Brackett series, given the limit for Lyman series is 911.6 Å.
Advertisements
Solution
Data: `lambda_("L"∞)` = 911.6 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_("Br"∞) = "R"_"H"(1/16 - 1/∞) = "R"_"H"/16` ......(4)
as n = 4 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)(911.6)` = 3646 Å
This is the series limit of the Balmer series.
From Eqs. (1) and (3), we get,
`lambda_("Pa"∞)/lambda_("L"∞) = "R"_"H"/("R"_"H"//9)` = 9
∴ `lambda_("Pa"∞) = 9lambda_("L"∞) = (9)(911.6)` = 8204 Å
This is the series limit of the Paschen series.
From Eqs. (1) and (4), we get,
`lambda_("Br"∞)/lambda_("L"∞) = "R"_"H"/("R"_"H"//16)` = 16
∴ `lambda_("Br"∞) = 16 lambda_("L"∞) = (16)(911.6)` = 14585.6 Å
This is the series limit of the Brackett series.
APPEARS IN
RELATED QUESTIONS
What is the shortest wavelength present in the Paschen series of spectral lines?
Determine the series limit of Balmer, Paschen, and Pfund series, given the limit for Lyman series is 912 Å.
In Balmer series, wavelength of first line is 'λ1' and in Brackett series wavelength of first line is 'λ2' then `lambda_1/lambda_2` is ______.
In the figure below, D and E respectively represent
If wavelength for a wave is `lambda = 6000 Å,` then wave number will be ____________.
Let the series limit for Balmer series be 'λ1' and the longest wavelength for Brackett series be 'λ2'. Then λ1 and λ2 are related as ______.
Which of the following transition will have highest emission frequency?
The energy (in eV) required to excite an electron from n = 2 to n = 4 state in hydrogen atom is ____________.
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?
If the mass of the electron is reduced to half, the Rydberg constant ______.
In hydrogen spectrum, the wavelengths of light emitted in a series of spectral lines is given by the equation, `1/lambda` = R `(1/4^2 - 1/"n"^2)`, where n = 5, 6, 7...... and 'R' is Rydberg's constant. Identify the series and wavelength region.
An electron makes a transition from orbit n = 4 to the orbit n = 2 of a hydrogen atom. What is the wave number of the emitted radiations? (R = Rydberg's constant)
To produce an emission spectrum of hydrogen it needs to be ______.
Show that the first few frequencies of light that is emitted when electrons fall to the nth level from levels higher than n, are approximate harmonics (i.e. in the ratio 1 : 2 : 3...) when n >> 1.
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 first three spectral lines of H-atom in the Balmer series are given λ1, λ2, λ3 considering the Bohr atomic model, the wavelengths of the first and third spectral lines `(lambda_1/lambda_3)` are related by a factor of approximately 'x' × 10–1. The value of x, to the nearest integer, is ______.
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 ______.
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 ______.
Find the wavelength and wave number of the first member of the Balmer series in Hydrogen spectrum. (`R =1.097xx10^7m^(-1)`)
The de-Broglie wavelength of the electron in the hydrogen atom is proportional to ______.
Calculate the wavelength of the first two lines in the Balmer series of hydrogen atoms.
