Saved Bookmarks
| 1. |
How are the quantam numbers n, l and m arrived at ? Explain the significance of these quantam numbers. |
|
Answer» Solution :To describe an electron completely four quantum numbers were predicted . They are (1) Principal quantum number , n (2) Azimuthal quantum number ,l (3) Magnetic quantum number , `m_(1)` and (4) Spin quantum number , `m_(s)`. a) Principal Quantum Number: 1) This was proposed by Neils Bohr . 2) It is denoted by the letter 'n'. 3) It represents the circular orbits around the nucleus. 4) As the value of n increases the size and energy of the orbit increases. 5) According to number method a has the values 1 , 2 , 3 ..... According to letter method 'n' can be represented by the letters K , L , M , .......... 6 ) In any orbit , the number of sub-orbits = n number of orbitals = `n^(2)` , 7 ) This Quantum number describes the size and energy of the orbit. b) Azimuthal Quantum Number : 1 ) This was proposed by Sommerfeld . 2) It is also known as Angular momentum quantum number . 3) It is denoted by the letter 'l'. 4) This quantum number represents the sub-levels present in the main levels. 5 ) The sub-levels are s , p , d and f . 6) The l values of s , p , d and f sub-levels are 0 , 1 , 2 ans 3 respectively . 7) This first main level contains only one sub-level and it is s . The second main level contains s , p sub-levels . The third main level contains s,p , d sub-levels . The fourth main level contains s, p d and f sub-levels.  8) The relative values of 1s, 2s,2p etc . can be calculate by adding up their n and 1 values . Ex :1 Energy value of 1s = 1 + 0 = 1 2. Energy value of 2p = 2 + 1 =3  3. Energy value of 3d = 3 + 2 = 5 4. Energy value of 4F = 4+3 = 7 9) This Quantum number describes the shape of the orbital .  C) Magnetic Quantum Number : 1) This was proposed by Lande . 2) It is denoted by the letter 'm' . 3) This quantum number describes the sub-sub levels of orbitals present in a GIVEN sub-level. 4) `'m_(1)'` has values from -l to + l through '0'. 5) The TOTAL number of 'm' values for given value of 'l' (2l+1) 6) All the orbitals present in a given sublevel possesses the same energy values because they possess the same n and l values . 7) This quantum number describes the orientation of the orbitals in space . d) Spin Quantum Number : 1) It was proposed by Uhlenbeck and Goudsmit. 2) It is denoted by `m_(s)` . 3) This quantum number describes the spin of the revolving electron . 4)`'m_(s)'` value of clockwise electron is`+1//2` and that of anticlockwise electron is`-1//2` . 5) Clockwise revolving electron is represented by `+1//2` and anticlockwise revolving electron is represented by `-1//2` . 6) This quantum number describes the direction of spin of the revolving electron. |
|