Explain the different types of spectral series.

When an electron in an excited state falls back to a lower energy state, it emits photon of particular energy which is equal to the difference in energies of two states. Rydberg formula gives a relation between energy difference between various energy levels and the wavelength of the photons. ν = R Z 2 1 n 1 2 - 1 n 2 2 where R is the Rydberg constant, Z is the atomic number and n 1 and n 2 are the principal quantum numbers of the orbit. The spectral lines are formed as a result of electronic transition from one energy level to another. For a hydrogen atom, these lines are divided into five series: (i) Lyman series: Lyman series is obtained when an electron jumps to the first orbit from any other outer orbit. The wavelengths of Lyman series lies in the ultraviolet region of the spectrum. (ii) Balmer series: Balmer series is obtained when an electron jumps to the second orbit from any other outer orbit. The wavelengths of Balmer series lies in the visible region of the spectrum. (iii) Paschen series: Paschen series is obtained when an electron jumps to the third orbit from any other outer orbit. The wavelengths of Paschen series lies in the infrared region of the spectrum. (iv) Brackett series: Brackett series is obtained when an electron jumps to the fourth orbit from any other outer orbit. The wavelengths of Brackett series lies in the infrared region of the spectrum. (v) Pfund series: This series is obtained when an electron jumps to the fifth orbit from any other outer orbit. The wavelengths of Pfund series lies in the infrared region of the spectrum.

Describe Rutherford atom model. What are the draw backs of this model?

In 1911 , Rutherford conducted an experiment in which he bombarded alpha particles on a thin gold foil. In that experiment, he observed that: (i) Most of the alpha particles passed straight through the gold foil. (ii) Very few particles scattered by more than 1 ° . (iii) About 1 in 8000 particles deflected by more than 90 ° . Based on these observations, he came up with a new model of atom. According to his model of the atom: (i) Most of the atom was empty space with its entire positive charge concentrated in a very small space inside the atom. This space was called the nucleus. (ii) The size of the nucleus is very small as compared to the size of the atom. (iii) The nucleus is surrounded by negatively charged particles called electrons. The negative charge of electrons is equal to the positive charge of the nucleus. Therefore, an atom is electrically neutral. (iv) Electrons revolve around the nucleus in circular orbits. Drawbacks of Rutherford's model of atom: (i) According to Rutherford's model of atom, electrons revolve around the nucleus in a circular path and are constantly under centripetal force. As a result, the electrons must undergo acceleration. Charged particles undergoing acceleration radiates energy, thus, electrons loses energy continuously and eventually falls into the nucleus. Thus, it failed to explain the stability of the atom. (ii) According to Rutherford's model, the atoms should emit continuous spectrum instead of line spectrum. Thus, it failed to explain the existence of spectral lines in the hydrogen spectrum.

What are the limitations of Bohr's theory of hydrogen atom?

Limitations of Bohr's theory: (i) Bohr's theory is limited to simple atoms like hydrogen for which Z = 1 . It fails for atoms of elements for which Z > 1 . (ii) It failed to explain the Zeeman effect i.e when the spectral line gets split into various components in the presence of magnetic field. (iii) It failed to explain the Stark effect i.e when the spectral line gets split into almost negligible lines in the presence of electric field. (iv) It violates Heisenberg uncertainty principle.

A difference of 2 . 3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

The Separation of two energy levels in an atom, E = 2 . 3 eV = 2 . 3 × 1 . 6 × 10 - 19 = 3 . 68 × 10 - 19 J The relation between energy and frequency is given by, E = h v Where, Planck’s constant h = 6 . 62 × 10 - 34 Js , and, ν is the frequency of radiation. ∴ ν = E ⁄ h = 3 . 68 × 10 - 19 6 . 62 × 10 - 34 = 5 . 55 × 10 14 Hz The radiation frequency is 5 . 6 × 10 14 Hz . Here, the symbols have their usual meaning.