Lesson2_1

# Lesson2_1 - Lesson 02 Atom MP200 Radiation Physics 2010...

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Lesson 02 Atom MP200 Radiation Physics - 2010 Duke Medical Physics Graduate Program 1

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Introduction A Brief History of Atom: Daltons Laws In the early 19th century, Dalton formulated his laws of the atom: 1. All elements are composed of atoms, which are indivisible and indestructible particles. 2. All atoms of a given element are identical; in particular, they all have the same mass. 3. All atoms of different elements are different; in particular, they have different masses. 4. Compounds are formed by the joining of atoms of two or more different kinds of elements. 5. A chemical reaction is a rearrangement of atoms. In the mid 19th century, study of the optical properties of elements showed that each element emits its own characteristic radiation with a series of lines. This was called line spectrum. In 1885 Balmer published his empirical formula that gave the wave length ( λ ) of radiation. In 1885, the Balmer equation for Hydrogen was, λ = 3646 n 2 ( n 2 - 4) where λ = wave length and n = integer Here, n = 3 is for H α and n = 4 for H β etc. In 1890, this was modified by Rydberg and his formula was 1 λ = R H ( 1 2 2 - 1 n 2 ) 2
where R H = 1 . 09737 × 10 7 m - 1 is the Rydberg constant The figure shows the line spectrum of atomic hydrogen. Figure 1: Spectrum of atomic Hydrogen The Balmer series is in the visible region of the electromagnetic spec- trum. In addition, there are four more series of the Hydrogen spectrum and following table shows these. Name Wave Length region Formula Lyman Ultraviolet 1 λ = R H ( 1 1 2 - 1 n 2 ) n = 2 , 3 , 4 , . . . Balmer Visible 1 λ = R H ( 1 2 2 - 1 n 2 ) n = 3 , 4 , 5 , . . . Paschen Infrared 1 λ = R H ( 1 3 2 - 1 n 2 ) n = 4 , 5 , 6 , . . . Brackett Infrared 1 λ = R H ( 1 4 2 - 1 n 2 ) n = 5 , 6 , 7 , . . . Pfund Infrared 1 λ = R H ( 1 5 2 - 1 n 2 ) n = 6 , 7 , 8 , . . . Early Atomic Models Thomson Model In 1897, J. J. Thomson discovered the electron and proposed an atomic model. 3

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In this model, It was assumed positive charge was spread throughout the atom, and electrons were suspended out of it. This was called the ” plum-pudding model”. In this model, there was no nucleus. Figure 2: Thomson Atomic Model Rutherford’s Planetary Model (1911) Rutherford’s α scattering on gold, experiment showed that atom was mostly empty space with small and dense nucleus. Electrons were orbiting around the nucleus. ( planetary model ) Problem with this model was that it could not explain physics. According to the classical physics, an electron in circular orbit accelerates. Accelerated electron radiates, and looses its energy, finally collapsing into the nucleus. Bohr’s Model of the Hydrogen Atom (1913) Combining Rutherford’s concept of the atom with Plank’s idea of quan- tized nature of radiative process Bohr developed an atomic model for Hydrogen like atoms. This model is based on four postulates. 4
An electron in an atom revolves around the nucleus in well-defined circular orbits under the influence of a Coulomb force between an electron and a positively charged nucleus. This force is balanced by the centripetal force. i.e. Coulomb force Ze 2 4 π 0 r 2 = mv 2 r

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