Advertisements
Advertisements
प्रश्न
Calculate the shortest wavelength in the Paschen series if the longest wavelength in the Balmar series is 6563 Ao.
Advertisements
उत्तर
Given:
(λB) = 6563 Å = 6563 × 10−10 m
= 6.563 × 10−7 m
To find: Shortest wavelength (λp)
Formula: `1/lambda = "R"[1/"n"^2 - 1/"m"^2]`
Calculation:
For (λB), m = 3, n = 2
From formula,
`1/lambda_"B" = "R"[1/2^2 - 1/3^2]`
`1/lambda_"B" = (5"R")/36`
∴ `lambda_"B" = 36/(5"R")` ....(1)
For Paschen series shortest wavelength (λp),
n = 3, m = ∞
∴ `1/lambda_"p" = "R"[1/3^2 - 1/∞]`
∴ `1/lambda_"p" = "R"[1/9]`
∴ `1/lambda_"p" = "R"/9`
∴ `lambda_"p" = 9/"R"` ....(2)
From equations (1) and (2),
`lambda_"p"/lambda_"B" = (9"/""R")/(36"/"5"R")`
∴ `lambda_"p"/lambda_"B" = 9/"R" xx (5"R")/36`
= `5/4`
∴ `lambda_"p" = 5/4 xx lambda_"B"`
= `5/4 xx 6563`
∴ λp = 8203.75 Å
The shortest wavelength in the Paschen series is 8203.75 Å.
संबंधित प्रश्न
The speed of electron having de Broglie wavelength of 10 -10 m is ______
(me = 9.1 × 10-31 kg, h = 6.63 × 10-34 J-s)
What is the energy of an electron in a hydrogen atom for n = ∞?
State any two limitations of Bohr’s model for the hydrogen atoms.
The angular momentum of an electron in the 3rd Bohr orbit of a Hydrogen atom is 3.165 × 10-34 kg m2/s. Calculate Plank’s constant h.
Calculate the wavelength for the first three lines in the Paschen series.
(Given RH =1.097 ×107 m-1)
Obtain an expression for wavenumber, when an electron jumps from a higher energy orbit to a lower energy orbit. Hence show that the shortest wavelength for the Balmar series is 4/RH.
Using Bohr's model, the orbital period of electron in hydrogen atom in nth orbit is (ε0 = permittivity of free space, h = Planck's constant, m = mass of electron and e = electronic charge)
Bohr model is applied to a particle of mass 'm' and charge 'q' is moving in a plane under the influence of a transverse magnetic field 'B. The energy of the charged particle in the nth level will be (h = Planck's constant).
The ratio of the velocity of the electron in the first orbit to that in the second orbit is ____________.
For which one of the following, Bohr model is not valid?
What is the de Broglie wavelength of an electron of energy 180 eV?
(Mass of electron = 9 x 10-31 kg and Planck's constant = 6.6 x 10-34 Js.)
The total energy of an electron in an atom in an orbit is -3.4 eV. Its kinetic and potential energies are, respectively ______.
In Bohr's model of hydrogen atom, the period of revolution of the electron in any orbit is proportional to ______.
When hydrogen atom is in its first excited level, its radius is how many time its ground state radius?
The binding energy of an electron in nth orbit of the hydrogen atom is given by `"E"_"n" = 13.6/"n"^2 "eV."` The energy required to knock an electron from the second orbit in eV will be ____________.
For an electron, discrete energy levels are characterised by ____________.
An electron of mass 'm' is rotating in first Bohr orbit of radius 'r' in hydrogen atom. The orbital acceleration of the electron in first orbit (h = Planck's constant).
In Bohr model, speed of electron in nth orbit of hydrogen atom is ______. (b = Planck's constant, n = principal quantum number, ∈0 is the permittivity of free space, e = electronic charge)
In Bohr's model of hydrogen atom, which of the following pairs of quantities are quantized?
Using Bohr's quantization condition, what is the rotational energy in the second orbit for a diatomic molecule. (I = moment of inertia of diatomic molecule, h = Planck's constant)
In any Bohr orbit of hydrogen atom, the ratio of K.E to P.E of revolving electron at a distance 'r' from the nucleus is ______.
The radius of orbit of an electron in hydrogen atom in its ground state is 5.3 x 10-11 m After collision with an electron, it is found to have a radius of 13.25 x 10-10 m. The principal quantum number n of the final state of the atom is ______.
The relation between magnetic moment of revolving electron 'M' and principle quantum number 'n' is ______.
An electron of mass m and charge e initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is ______.
The radius of the first Bohr orbit in the hydrogen atom is 0.5315 Å. The radius of the second Bohr orbit in the hydrogen atom is ______.
