Advertisements
Advertisements
Question
What is the minimum energy that must be given to a H atom in ground state so that it can emit an Hγ line in Balmer series. If the angular momentum of the system is conserved, what would be the angular momentum of such Hγ photon?
Advertisements
Solution
We know that Hγ spectral line in the Balmer series is formed when an electron falls from n = 5 to n = 1.
Here the electron is in the ground state ie., n = 1 and must be taken to n = 5 for Hγ line.
So the energy of H? = `E_5 - E_1 = (13.6/5^2) - (- 13.6)`
= – 0.54 + 13.6
= 13.06 eV
Since angular momentum, is conserved, so the angular momentum of Hγ = change in angular momentum of the electron
= L5 – L2 – 5h – 2h
= 3h = 3 × 6.63 × 10–34
= 19.89 × 10–34 kg m2/s
APPEARS IN
RELATED QUESTIONS
In both β− and β+ decay processes, the mass number of a nucleus remains the same, whereas the atomic number Z increases by one in β− decay and decreases by one in β+ decay. Explain giving reason.
In Balmer series, wavelength of first line is 'λ1' and in Brackett series wavelength of first line is 'λ2' then `lambda_1/lambda_2` is ______.
If wavelength for a wave is `lambda = 6000 Å,` then wave number will be ____________.
Let v1 and v3 be the frequency for series limit of Balmer and Paschen series respectively. If the frequency of first line of Balmer series is v2 then, relation between v1 and v2 and v3 is ____________.
The radii of the first four Bohr orbits of hydrogen atom are related as ____________.
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.
Each element is associated with a ______.
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.
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.
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.)
Determine the shortest wavelengths of Balmer and Pasch en series. Given the limit for the Lyman series is 912 Å.
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 ______.
