Model-of-Hydrogen-Atom

PHYSICS CHAPTER 11 1 CHAPTER 11: CHAPTER 11: Bohr’s model of hydrogen atom Bohr’s model of hydrogen atom (3 Hours) (3 Hours) PHYSICS CHAPTER 11 2 At the end of this chapter, students should be able to: At the end of this chapter, students should be able to:  Explain Explain Bohr’s postulates of hydrogen atom. Bohr’s postulates of hydrogen atom. Learning Outcome: www.kmph.matrik.edu.my/physics www.kmph.matrik.edu.my/physics 11.1 Bohr’s atomic model (1 hour) PHYSICS CHAPTER 11 3 11.1.1 Early models of atom Thomson’s model of atom Thomson’s model of atom  In 1898, Joseph John Thomson suggested a model of an atom that consists of homogenous positively charged spheres with tiny negatively charged electrons embedded throughout the sphere as shown in Figure 11.1.  The electrons much likes currants in a plum pudding.  This model of the atom is called ‘plum pudding’ model of the atom. 11.1 Bohr’s atomic model positively charged sphere electron Figure 11.1 Figure 11.1 PHYSICS CHAPTER 11 4 Rutherford’s model of atom Rutherford’s model of atom  In 1911, Ernest Rutherford performed a critical experiment that showed the Thomson’s model is not correct and proposed his new atomic model known as Rutherford’s planetary model of the atom as shown in Figure 11.2a.  According to Rutherford’s model, the atom was pictured as electrons orbiting around a central nucleus which concentrated of positive charge.  The electrons are accelerating because their directions are constantly changing as they circle the nucleus. nucleus electron Figure 11.2a Figure 11.2a PHYSICS CHAPTER 11 5  Based on the wave theory, an accelerating charge emits energy.  Hence the electrons must emit the EM radiation as they revolve around the nucleus.  As a result of the continuous loss of energy, the radii of the electron orbits will be decreased steadily.  This would lead the electrons spiral and falls into the nucleus, hence the atom would collapse as shown in Figure 11.2b. Figure 11.2b Figure 11.2b + +Ze − − e e ‘plop’ energy loss PHYSICS CHAPTER 11 6 +e − − e v  r e F   In 1913, Neils Bohr proposed a new atomic model based on hydrogen atom.  According to Bohr’s Model, he assumes that each electron each electron moves in a circular orbit which is centred on the nucleus moves in a circular orbit which is centred on the nucleus, the necessary centripetal force being provided by the centripetal force being provided by the electrostatic force of attraction between the positively electrostatic force of attraction between the positively charged nucleus and the negatively charged electron charged nucleus and the negatively charged electron as shown in Figure 11.3. 11.1.2 Bohr’s model of hydrogen atom Figure 11.3 Figure 11.3 PHYSICS CHAPTER 11 7  On this basis he was able to show that the energy of an energy of an orbiting electron depends on the radius of its orbit orbiting electron depends on the radius of its orbit.  This model has several features which are described by the postulates (assumptions) stated below : 1. The electrons electrons move only in certain circular orbits, called STATIONARY STATES STATIONARY STATES or ENERGY LEVELS ENERGY LEVELS. When it is in one of these orbits, it does not radiate energy does not radiate energy. 2. The only permissible orbits are permissible orbits are those in the discrete set for which the angular momentum of the electron angular momentum of the electron L L equals an integer times equals an integer times h/ h/ 2 2 π π . Mathematically, π 2 nh L = π 2 nh mvr = (11.1) (11.1) and mvrL = where orbit theof radius: r electron theof mass:m , ,,n 321number quantum principal: = PHYSICS CHAPTER 11 8 3. Emission or absorption Emission or absorption of radiation occurs only when an electron makes a transition from one orbit to another electron makes a transition from one orbit to another. The frequency f of the emitted (absorbed) radiation is given by if EEhfE −==∆ (11.2) (11.2) where constant sPlanck': h stateenergy final: f E energy of change: E ∆ stateenergy initial: i E Note: Note:  If E f > E i  If E f < E i Emission Emission of EM radiation Absorption Absorption of EM radiation PHYSICS CHAPTER 11 9 At the end of this chapter, students should be able to: At the end of this chapter, students should be able to:  Derive Derive Bohr’s radius and energy level in hydrogen atom. Bohr’s radius and energy level in hydrogen atom.  Use Use  Define Define ground state energy, excitation energy and ground state energy, excitation energy and ionisation energy. ionisation energy. Learning Outcome: www.kmph.matrik.edu.my/physics www.kmph.matrik.edu.my/physics 11.2 Energy level of hydrogen atom (1 hour)       == 22 2 0 2 4 mke h nanr n π and and       −= 2 0 2 1 2 n a ke E n PHYSICS CHAPTER 11 10 11.2.1 Bohr’s radius in hydrogen atom  Consider one electron of charge –e and mass m moves in a circular orbit of radius r around a positively charged nucleus with a velocity v as shown in Figure 11.3.  The electrostatic force between electron and nucleus electrostatic force between electron and nucleus contributes the centripetal force contributes the centripetal force as write in the relation below: 11.2 Energy level of hydrogen atom ce FF = centripetal force electrostatic force r mv r QQ 2 2 21 0 4 1 =       πε and eQQ == 21 r e mv 0 2 2 4 πε = (11.3) (11.3)