Advertisements
Advertisements
प्रश्न
The ground state energy of hydrogen atom is −13.6 eV. If an electron make a transition from an energy level −0.85 eV to −1.51 eV, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum does this wavelength belong?
उत्तर
Since energy of Hydrogen atom is given as
`E_n = (-13.6)/n^2 eV`
Ground state energy E1 = −13.6eV
Now electron makes a transition from energy level
np = −0.85 eV to nq = −1.51 eV
Now,
`E_(n_p) = (-13.6)/n_p^2 eV`
`n_p^2 = (-13.6)/-0.85 = 16`
`n_p = 4`
Again,`E_(n_p) = (-13.6)/n_q^2 eV`
`n_p^2 = (-13.6)/(-1.51) =9`
`n_q = 3`
Thus, we have transition from n = 4 to n = 3.
Since transition corresponds to the transition of an electron from some higher energy state to an orbit having n = 3. It is Paschen series of the hydrogen spectrum. Wavelength is given as
`1/lambda = R(1/3^2 - 1/x^2)`
Where R is Rydberg’s constant
`R = 1.097 xx 10^7 m^-1 1/lambda = 1.097 xx 10^7 [1/9 - 1/16]`
`= 1.097 xx 10^7 [7/(9 xx 16)]`
`lambda = (9 xx 16)/(1.097 xx 10^7 xx 7) = 18.752 xx 19^-7 m = 1875 nm`
APPEARS IN
संबंधित प्रश्न
When is Hα line in the emission spectrum of hydrogen atom obtained? Calculate the frequency of the photon emitted during this transition.
The ground state energy of hydrogen atom is – 13∙6 eV. If an electron makes a transition from an energy level – 1∙51 eV to – 3∙4 eV, calculate the wavelength of the spectral line emitted and name the series of hydrogen spectrum to which it belongs.
Using Rydberg formula, calculate the longest wavelength belonging to Lyman and Balmer series. In which region of hydrogen spectrum do these transitions lie?
[Given R = 1.1 ✕ 107 m−1]
In a laboratory experiment on emission from atomic hydrogen in a discharge tube, only a small number of lines are observed whereas a large number of lines are present in the hydrogen spectrum of a star. This is because in a laboratory
A spectroscopic instrument can resolve two nearby wavelengths λ and λ + Δλ if λ/Δλ is smaller than 8000. This is used to study the spectral lines of the Balmer series of hydrogen. Approximately how many lines will be resolved by the instrument?
Name the series in the atomic spectra of the hydrogen atom that falls in the ultra violet region.
The short wavelength limit for the Lyman series of the hydrogen spectrum is 913.4 Å. Calculate the short wavelength limit for the Balmer series of the hydrogen spectrum.
In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.
The transitions A, B and C respectively represents
A particular hydrogen-like ion emits radiation of frequency 2.92 × 1015 Hz when it makes the transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be ______.
Name the series of lines of hydrogen spectrum which lie in the visible region.
