Line spectrum (contd.) Bohr s Planetary Atom

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1 Line spectrum (contd.) Hydrogen shows lines in the visible region of the spectrum (red, blue-green, blue and violet). The wavelengths of these lines can be calculated by an equation proposed by J. J. Balmer: This equation only works with the H atom In this equation n is an integer >..097 x 0 7 m - is known as the Rydberg constant. For n =, λ = 6.56 x 0-7 m = 656 nm (corresponds to red). Calculate the other wavelengths for the line spectrum of hydrogen. Bohr s Planetary Atom Accepted idea was the presence of a dense nucleus in the middle containing the protons and neutrons and a diffuse region around it containing the electrons. Could not explain atomic stability Niels Bohr proposed a more orderly view of the atom where the electrons occupied certain fixed paths around the nucleus. Each of these paths was called an orbit (or energy level) and had a fixed value of energy. Each orbit could be identified by either a letter or a number (this number is called the principal quantum number)

2 Orbits Nucleus More Bohr By extending the concept of energy quantization the energy of each orbit could be expressed by the formula R H is a constant and =.79 x 0-8 J and n is the principal quantum number which can have values from.....

3 Orbits and Quantum Numbers Electrons occupy orbits. There are an infinite number of orbits possible. Each of these orbits is at a fixed distance (radius) from the nucleus and has a fixed value of energy. The orbit that is closest to the nucleus has the lowest energy. Each of these levels can be pictured as concentric circles surrounding the nucleus. 5 rd Orbit Nucleus nd Orbit st Orbit 6

4 Orbits and Quantum Numbers Electrons can move from a level of lower energy to another level with higher energy by absorbing energy. This process called excitation produces the excited state of that atom. Relaxation is the exact opposite process, where an electron moves from a higher energy level to a lower energy level accompanied by a release of energy. 7 Energy and Transitions The energy (in the form of light) emitted by an electron in the relaxation process can be calculated by the formula: When you substitute R H =.79 x 0-8 J, h = 6.66 x 0 - J s and c =.00 x 0 8 m/s, the term R H /hc =.097 x 0 7 m - (Rydberg constant). What wavelength of light is emitted when an electron in an atom undergoes a transition from n = to n =? Here n f =, n f = and we can use the above formula to calculate the value of λ. 8

5 Energy and Transitions (contd.) The energy associated with this wavelength can be easily found. 9 Quantum Numbers Each orbit can be described by assigning a letter or a number to it. The number (which can never be zero) is known as the principal quantum number n and describes the position and the energy of that orbit. Orbit First Second Third Fourth Letter K L M N Value of n Increasing Energy 0 5

6 M, n = Nucleus L, n = K, n = Quantum Mechanical Atom Bohr s atom put severe restrictions on the location of electrons. Heisenberg (in his uncertainty principle) proposed and proved that at a given time, the location and the energy of an electron, can t be determined simultaneously. Instead of orbits (fixed paths) we now measure the possibility (probability) of an electron being in a certain region within the orbits at a given time. 6

7 Schrödinger & Quantum mechanics Information about an electron in a given energy level in an atom is described by a wave function (Ψ, psi). The probability of finding an electron in a certain region around the nucleus is given by Ψ. This is also known as an atomic orbital. The value of Ψ decreases rapidly as we move away from the nucleus, it is never zero. This indicates that there is no fixed boundary for an atom (unlike the Bohr model). Quantum Mechanical Atom Each orbit (principal energy level) is further divided into subshells and each subshell consists of one or more atomic orbitals. The # of subshells in each level = principal quantum number n. Thus: Orbit n # of subshells First Second Third Fourth 7

8 Quantum numbers Principal (n): the number on which the energy of the electron depends. The smaller the value of n, lower the energy. The larger the value of n, the larger the orbit. Can have any value from,,,. Angular momentum quantum number (l): distinguishes orbitals of a given n having different shapes. Can have any value from 0,,, n. A subshell within a shell is denoted by writing the value for n followed by the type of subshell. p denotes n = and l = Value of n Value of l 0 Values of l Type of subshell 5 Subshells Subshells are symbolized by s, p, d and f. Energy wise s < p < d < f n # of subshells Types of subshells # of electrons (n) s x ( ) = s and p x ( ) = s, p and d x ( ) = s, p, d and f x ( ) = 6 8

9 Orbitals and their shapes An orbital is a specific region of a subshell containing a maximum of electrons. Orbitals are of different shapes and have different orientations in space. The s orbital is spherical in shape. There can be only one s orbital in each subshell. p orbitals are propeller shaped and are aligned along the different axes. Depending on the axis they are aligned with these are labeled p x, p y and p z. (See figure 6.0 from our book). There are five d orbitals possible (n ) and there are seven f orbitals possible when n. 7 Orbitals and # of Electrons An orbital is defined as a specific region of a subshell containing a maximum of electrons. Each orbital = electrons. n # of subshells Types of subshells # of electrons s s, p x, p y, p z s, p x,p y, p z and 5 types of d s, p, d and f 8 9

10 Quantum numbers Magnetic quantum number (m l ): distinguishes orbitals of a given n and l, but having different orientations in space. Values range from l,,0,, +l. n l m l 0 (s) 0 0 (s) (p) 0 -, 0, + 0 (s) (p) (d) 0 -, 0, + -, -, 0, +, + 0 (s) (p) (d) (f) 0 -, 0, + -, -, 0, +, + -, -, -, 0, +, +, + 9 Spin Each electron is assigned a spinning motion along an imaginary axis. The electrons present in each orbital must spin in opposite directions; clockwise and anticlockwise. A pair of electrons in an orbital with opposite spins are called paired. Clockwise Anticlockwise 0 0