Emission spectrum of hydrogen

This would enable students to explain the emission spectrum of hydrogen using the Bohr model of the hydrogen atom; calculate the energy, wavelength, and frequencies involved in the electron transitions in the hydrogen atom; relate the emission spectra to common occurrences like fireworks and neon lights; and describe the Bohr model of the atom and the inadequacies of the Bohr model.

1. Emission Spectrum of Hydrogen, and Dual Nature of Matter Prepared by: Mrs. Eden C. Sanchez

2. Learning Objectives: Explain the emission spectrum of hydrogen using the Bohr model of the hydrogen atom Calculate the energy, wavelength, and frequencies involved in the electron transitions in the hydrogen atom. Relate the emission spectra to common occurrences like fireworks and neon lights . Describe the Bohr model of the atom and the inadequacies of the Bohr model.

3. Learning Objectives: Explain the wave-particle duality of matter

4. Keywords a. Emission spectrum b. Rydberg’s constant c. Ground state d. Ground energy level e. Excited state f. Excited energy level g. Travelling wave h. Standing wave i. De Broglie Equation

5. THE EMISSION SPECTRUM AND THE BOHR THEORY OF THE HYDROGEN ATOM When elements are energized by heat or other means, they give off a characteristic or distinctive spectrum , called an emission spectrum , which can be used to differentiate one element from another. While scientists recognized the usefulness of emission spectra in identifying elements, the origins of these spectra were unknown.

6. From Rutherford’s theory, the atom was described to be mostly empty space having a very tiny but dense nucleus that contained the protons. The electrons whirled around the nucleus in circular orbits at high velocities.

7. Classical mechanics and electromagnetic theory explained that any charged particle moving on a curved path would emit electromagnetic radiation. This implies that electrons would lose energy and spiral into the nucleus.

8. In 1913, Niels Bohr proposed his model of the hydrogen atom to explain how electrons could stay in stable orbits around the nucleus. This model is no longer considered to be correct in all its details. However , it could explain the phenomenon of emission spectra. For his model of the hydrogen atom, Bohr made the following postulates:

9. Electrons go around the nucleus in circular orbits. However, not all circular orbits are allowed. The electron is allowed to occupy only specific orbits with specific energies. Therefore, the energies of the electron are quantized. If the electron stays in the allowed orbit, its energy is stable. It will not emit radiation and it will not spiral into the nucleus .

10. If an electron jumps from one orbit to another, it will absorb or emit energy in quanta equal to ∆E = hv h (Planck’s constant) = 6.626 X 10 -34 J s

11. According to Bohr, the energy of the electron in the H atom is given by: The negative sign is an arbitrary convention. A free electron is arbitrarily considered to have an energy of zero. A negative energy means that the energy of the electron is lower than the energy of a free electron .

12. R H is the Rydberg constant for hydrogen equal to 2.18 x 10 -18 J .

13. Exercises What is the energy of the electron when it is in the first orbit, n=1 ? What is the energy of the electron in orbit n = 2 ? What is the energy of the electron in orbit n = 3 ? In which orbit will the electron have the highest energy, n=1, n=2, or n=3?

14. Exercises As the value of n increases, what happens to the energy value of the electron?

15. E 1 is the lowest energy and , the most stable state. It is called the ground state or the ground level. E 2 , E 3 , E 4 , etc. have higher energies and are less stable than E 1 . They are called excited states or excited levels . Note also that as the electron gets closer to the nucleus, it becomes more stable .

16. When energy is absorbed by the atom, the electron gets excited and jumps from a lower orbit to a higher orbit. When electrons go from a higher energy level to a lower energy level , it emits radiation . According to Bohr, if an electron jumps from one orbit to another, it will absorb or emit energy in quanta equal to:

17. Bohr model explains the experimental emission spectrum of hydrogen which includes a wide range of wavelengths from the infrared to the UV region. Series n final n initial Spectrum Region Lyman 1 2,3,4 ultraviolet Balmer 2 3,4,5 visible & ultraviolet Paschen 3 4,5,6 infrared Brackett 4 5,6,7 infrared

18. Exercises 1. The electron in the hydrogen atom undergoes a transition from n=3 to n=2. Is energy absorbed or emitted? What is the energy involved in the transition? What is the wavelength (in nm) corresponding to this transition? What region of the electromagnetic spectrum will this be ?

19. Exercises 2. Which transition of the electron in the hydrogen atom will involve the highest frequency ? n = 5 to n = 3 n = 4 to n = 3 n = 5 to n = 2

20. THE LIMITATIONS OF THE BOHR MODEL OF THE ATOM It cannot explain the spectrum of atoms with more than one electron. It cannot explain the relative intensities of spectral lines (why are some lines more intense than others ) It cannot explain why some lines are slit into several components in the presence of a magnetic field (called the Zeeman effect)

21. According to the Bohr model, when electrons go around the nucleus in certain orbits, its energy remains constant. But moving electrons would lose energy by emitting electromagnetic waves and the electron is expected to spiral into the nucleus. It violates the Heisenberg’s Uncertainty Principle. The Bohr model considers electrons to have a known radius and orbit which is impossible according to Heisenberg.

22. THE DUAL NATURE OF THE ELECTRON: DE BROGLIE’S EQUATION In 1924, Louis de Broglie made a bold proposition based on Planck’s and Einstein’s concepts. De Broglie reasoned that if light could have particle-like properties , then particles like electrons could also have wavelike properties. De Broglie’s idea – if the electron going around the nucleus in a circular orbit behaves as a wave, then it should behave as a standing wave . In a standing wave, there are fixed points, or nodes, where the amplitude is zero.

23. De Broglie’s particle and wave properties is given by the De Broglie equation :

24. Where h is Planck’s constant, m is the mass of the particle, and u is the velocity. Therefore , a particle in motion can be treated as a wave and a wave can exhibit properties of a particle. An electron has both particle and wavelike properties – this is referred as the dual nature of matter.

25. EXPERIMENTAL EVIDENCE OF DE BROGLIE WAVELENGTH Waves associated with material particles were called by de Broglie as “matter waves”. If matter waves exist for small particles, then beams of particles, such as electrons, should exhibit the properties of waves, like diffraction .

26. Diffraction refers to various phenomena which occur when a wave encounters an obstacle or a slit . In classical physics, the diffraction phenomenon is described as the interference of waves . If the distance between objects that the waves scatter from is about the same as the wavelength of the radiation, diffraction occurs and an interference pattern occurs.

27. Flame test One method of demonstrating the emission spectrum of substances through a qualitative analysis In this technique, a small amount of substance is heated. The heat of the flame excites the electrons of the metals ions, causing them to emit visible light the color of which is unique to the metal ion.

28. Flame colors Metal ion Flame color Li Red Na Yellow K Lilac Ca Orange/Yellow-red Sr Red Ba Pale green Cu Blue green