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
What is the shortest wavelength present in the Paschen series of spectral lines?
In the figure below, D and E respectively represent
Which of the following transition will have highest emission wavelength?
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 ____________.
In hydrogen spectrum, which of the following spectral series lies in ultraviolet region?
The radii of the first four Bohr orbits of hydrogen atom are related as ____________.
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.
Continuous spectrum is produced by ______.
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)
Absorption line spectrum is obtained ______.
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?
The first four spectral lines in the Lyman series of a H-atom are λ = 1218 Å, 1028Å, 974.3 Å and 951.4 Å. If instead of Hydrogen, we consider Deuterium, calculate the shift in the wavelength of these lines.
Determine the shortest wavelengths of Balmer and Pasch en series. Given the limit for the Lyman series is 912 Å.
Determine the series limit of Balmer, Paschen and Brackett series, given the limit for Lyman series is 911.6 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 ______.
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 ______.
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 ______.
