Advertisements
Advertisements
प्रश्न
Compute the shortest and the longest wavelength in the Lyman series of hydrogen atom.
Find the shortest and longest wavelengths in the Lyman series of hydrogen atom.
Advertisements
उत्तर
Given: R = 1.097 × 107 m−1
`1/λ = R_H (1/(n^2) - 1/(m^2))`
For the Lyman series, n = 1 and for the shortest wavelength, m = ∞.
∴ `1/(λ) = R (1/1^2 - 1/∞^2) = R`
∴ The short wavelength limit of the Lyman series,
`λ = 1/R`
= `1/(1.097 xx 10^7)`
= 0.9110 × 10−7 m
= 911 Å
For the longest wavelength in the Lyman series, n = 1 and m = 2.
∴ `1/(λ) = R (1/1^2 - 1/2^2)`
= `R (1/1 - 1/4)`
= `R ((4 - 1)/4)`
= `(3R)/4`
= `(3(1.097 xx 10^7))/4`
∴ The wavelength of the first Lyman line,
`1/λ = 4/3.291 xx 10^-7`
= 1.215 × 10−7 m
= 1215 Å
APPEARS IN
संबंधित प्रश्न
Linear momentum of an electron in Bohr orbit of H-atom (principal quantum number n) is proportional to ______.
Answer in brief.
State the postulates of Bohr’s atomic model.
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 = ∞?
Using de Broglie’s hypothesis, obtain the mathematical form of Bohr’s second postulate.
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.
How the linear velocity 'v' of an electron in the Bohr orbit is related to its quantum number 'n'?
The magnifying power of a telescope is high, if its objective and eyepiece have respectively ____________.
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).
Taking the Bohr radius as a0= 53 pm, the radius of Li++ ion in its ground state, on the basis of Bohr's model, will be about ______.
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.)
If m is mass of electron, v its velocity, r the radius of stationary circular orbit around a nucleus with charge Ze, then from Bohr's second postulate, the kinetic energy `"K.E." = 1/2"mv"^2` of the electron in C.G.S. system is 2 equal to ____________.
When an electron in hydrogen atom is excited from its 3rd to 5th stationary orbit, tbe change in angular momentum of electron is (Planck's constant: h = 6.62 x 10-34 Js) ____________.
In hydrogen spectnun, the wavelengths of light emited in a series of spectral lines is given by the equation `1/lambda = "R"(1/3^2 - 1/"n"^2)`, where n = 4, 5, 6 .... And 'R' is Rydberg's constant.
Identify the series and wavelenth region.
Ratio of centripetal acceleration for an electron revolving in 3rd orbit to 5th orbit of hydrogen atom is ______.
In Bohr's model of hydrogen atom, which of the following pairs of quantities are quantized?
If a charge on the body is 1 nC, then how many electrons are present on the body?
If n is principal quantum number and r is the radius of the orbit in which electron revolves around nucleus, then its kinetic energy 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 ______.
If Vn and Vp are orbital velocities in nth and pth orbit respectively, then the ratio Vp: Vn is ______.
The ground state energy of the hydrogen atom is -13.6 eV. The kinetic and potential energy of the electron in the second excited state is respectively ______
What is the mathematical formula for the third postulate of Bohr's atomic model?
Which of the following series of transition of hydrogen spectrum falls in visible region?
The value of Rydberg constant in joule is ______.
Ultraviolet light of wavelength 300 nm and intensity 1.0 Wm−2 falls on the surface of a photosensitive material. If one percent of the incident photons produce photoelectrons, then the number of photoelectrons emitted from an area of 1.0 cm2 of the surface is nearly ______.
Calculate the energy of the electron in the ground state of the hydrogen atom. Express it in joule and in eV.
Find the ratio of radius of 1st Bohr orbit to that of 4th Bohr orbit.
