Advertisements
Advertisements
प्रश्न
Using an expression for energy of electron, obtain the Bohr’s formula for hydrogen spectral lines.
Advertisements
उत्तर
Suppose an electron jumps from nth higher orbit to pth lower orbit.
Let and En Ep be the energies of electron in nth and pth orbit respectively.
`therefore` Energy of electron in nth orbit is, En = `-((me^4)/(8ε_0^2h^2))=1/2.............(1)`
`therefore` Energy of electron in pth orbit , Ep =`-((me^4)/(8ε_0^2h^2))1/P^2..............(2)`
`therefore` According to Bohr’s 3rd postulate, energy emitted is given by,
`therefore` energy emitted, `hnu =E _n-E_p`
`therefore` `hnu = (me^4)/(8ε_0^2h^2)(1/p^2-1/n^2)`
Or `nu = (me^4)/(8ε_0^2h^3)(1/p^2-1/n^2)`
`therefore 1/lambda=(me ^4)/(8ε_0^2h^3C)(1/p^2-1/n^2)` `[because nu = C/lambda]`
`therefore 1/lambda="R"(1/p^2-1/n^2)`
Where, `"R" = (me ^4)/(8ε_0^2ch_3)` is called Rydberg’s constant.
APPEARS IN
संबंधित प्रश्न
The nuclei having same number of protons but different number of neutrons are called ___ .
(a) isobars
(b) a-particles
(c) isotopes
(d) y-particles
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.
Calculate the minimum wavelength of the spectral line present in Balmer series of hydrogen
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]
Using Rydberg formula, calculate the wavelengths of the spectral lines of the first member of the Lyman series and of the Balmer series.
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?
Name the series in the atomic spectra of the hydrogen atom that falls in the ultra violet region.
When a beam of white light is passed through sodium vapors and then through a spectrometer, spectrum so obtained has two dark lines present in the yellow region. This spectrum is called:
Hydrogen spectrum consists of discrete bright lines in a dark background and it is specifically known as hydrogen emission spectrum. There is one more type of hydrogen spectrum that exists where we get dark lines on the bright background, it is known as the absorption spectrum. Balmer found an empirical formula by the observation of a small part of this spectrum and it is represented by
`1/lambda = "R"(1/2^2 - 1/"n"^2)`, where n = 3, 4, 5,....
For Lyman series, the emission is from first state to nth state, for Paschen series, it is from third state to nth state, for Brackett series, it is from fourth state to nth state and for P fund series, it is from fifth state to nth state.
Which series of hydrogen spectrum corresponds to ultraviolet region?
Hydrogen spectrum consists of discrete bright lines in a dark background and it is specifically known as hydrogen emission spectrum. There is one more type of hydrogen spectrum that exists where we get dark lines on the bright background, it is known as absorption spectrum. Balmer found an empirical formula by the observation of a small part of this spectrum and it is represented by
`1/lambda = "R"(1/2^2 - 1/"n"^2)`, where n = 3, 4, 5,....
For Lyman series, the emission is from first state to nth state, for Paschen series, it is from third state to nth state, for Brackett series, it is from fourth state to nth state and for P fund series, it is from fifth state to nth state.
Which of the following lines of the H-atom spectrum belongs to the Balmer series?
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.
An electron in a hydrogen atom makes transitions from orbits of higher energies to orbits of lower energies.
- When will such transitions result in (a) Lyman (b) Balmer series?
- Find the ratio of the longest wavelength in the Lyman series to the shortest wavelength in the Balmer series.
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 ultraviolet region.
Name the series of lines of hydrogen spectrum which lie in the visible region.
In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series is ______.
Match List I with List II.
| List-I (Spectral Lines of Hydrogen for transitions from) |
List-II (Wavelengths (nm)) |
||
| A. | n2 = 3 to n1 = 2 | I. | 410.2 |
| B. | n2 = 4 to n1 = 2 | II. | 434.1 |
| C. | n2 = 5 to n1 = 2 | III. | 656.3 |
| D. | n2 = 6 to n1 = 2 | IV. | 486.1 |
Choose the correct answer from the options given below:
The longest wavelength associated with Paschen series is ______.
(Given: RH = 1.097 × 107 SI unit)
If an electron in hydrogen atom jumps from 3rd orbit to 2nd orbit it emits a photon of wavelength λ. When it emits a photon from 4th orbit to 3rd orbit then the corresponding wavelength of emitted photon will be ______.
The electron in hydrogen atom is initially in the 4th excited state. When it finally moves to ground state, the maximum number of spectral lines emitted are ______.
