Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let µH and µD be the reduced masses of electrons for hydrogen and deuterium respectively.
We know that `1/λ = R[1/n_f^2 - 1/n_1^2]`
As ni and nf are fixed for by mass series for hydrogen and deuterium.
`λ ∝ 1/R` or `λ_D/λ_H = R_H/R_D` ......(i)
`R_R = (m_ee^4)/(8ε_0ch^3) = (µ_He^4)/(8ε_0ch^3)`
`R_D = (m_ee^4)/(8ε_0ch^3) = (µ_De^4)/(8ε_0ch^3)`
∴ `R_H/R_D = µ_H/µ_D` ......(ii)
From equations (i) and (ii)
`λ_D/λ_H = µ_H/µ_D` ......(iii)
Reduced mass for hydrogen,
`µ_H = m_e/(1 + m_e/M) ≃ m_e(1 - m_e/M)`
Reduced mass for deuterium,
`µ_D = (2M * m_e)/(2M(1 + m_e/(2M))) ≃ m_e(1 - m_e/M)`
Where M is the mass of proton
`µ_H/µ_D = (m_e(1 - m_e/(2M)))/(m_e(1 - m_e/(2M))) = (1 - m_e/M)(1 - m_e/(2M))^-1`
= `(1 - m_e/M)(1 + m_e/(2M))`
⇒ `µ_H/µ_D = (1 - m_e/(2M))`
or `µ_H/µ_D = (1 - 1/(2 xx 1840))` = 0.99973 .....(iv) (∵ M = 1840 me)
From (iii) and (iv)
`λ_D/λ_H` = 0.99973, λD = 0.99973 λH
Using λH = 1218 Å, 1028 Å, 974.3 Å and 951.4 Å, we get
λD = 1217.7 Å, 1027.7 Å, 974.04 Å, 951.1 Å
Shift in wavelength (λH – λD) = 0.3 Å.
APPEARS IN
संबंधित प्रश्न
What is the shortest wavelength present in the Paschen series of spectral lines?
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 ______.
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.
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.
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.)
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 ______.
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 ______.
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.
