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Chapter 7: Problem 32

The periodic table consists of four blocks of elements that cor- respond to \(s, p, d,\) and \(f\) orbitals being filled. After \(f\) orbitals come \(g\) and \(h\) orbitals. In theory, if a \(g\) block and an \(h\) block of elements existed, how long would the rows of \(g\) and \(h\) elements be in this theoretical periodic table?

Short Answer

Expert verified
In a theoretical periodic table with 'g' and 'h' orbitals, the 'g' block rows would consist of 18 elements, while the 'h' block rows would consist of 22 elements. This is determined by calculating the maximum number of electrons that can be held by the respective orbitals using the formula \( 2(2l + 1) \), where l is the azimuthal quantum number.

Step by step solution

01

Determine the 'g' block element rows length

To find the length of the 'g' block element rows, we need to calculate the number of electrons that can be held by the 'g' orbitals. The 'g' orbitals follow the 'f' orbitals in the order, so they will hold more electrons than the 'f' orbitals. The general rule is that the maximum number of electrons that can be accommodated in a set of orbitals with a given azimuthal quantum number l is given by: \( 2(2l + 1) \) For 'g' orbitals, the azimuthal quantum number l is 4 (s - 0, p - 1, d - 2, f - 3, g - 4). Now let's apply the formula to find the maximum electrons that can be held by 'g' orbitals: \( 2(2(4) + 1) = 2(9) = 18 \) The 'g' block would consist of 18 elements in a row.
02

Determine the 'h' block element rows length

Similarly, we can determine the number of elements in the 'h' block element rows by calculating the number of electrons that can be held by the 'h' orbitals. The 'h' orbitals follow the 'g' orbitals in the order, so they will hold more electrons than the 'g' orbitals. For 'h' orbitals, the azimuthal quantum number l is 5 (s - 0, p - 1, d - 2, f - 3, g - 4, h - 5). Now let's apply the formula to find the maximum electrons that can be held by 'h' orbitals: \( 2(2(5) + 1) = 2(11) = 22 \) The 'h' block would consist of 22 elements in a row. In conclusion, in this theoretical periodic table, the 'g' block rows would be 18 elements long, and the 'h' block rows would be 22 elements long.

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