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I'll explain my thought process of getting to the elements from the electron configuration. In these four examples, the textbook is using shorthand notation in which they are using noble gas core just to shorten up the electron configuration (otherwise you would have to write out every single orbital which would be too long). For the first case, the noble gas core is Kr. 4d^10 represents that the 4d orbital is completely filled and 5s^2 represents that the 5s orbital is completely full. Remember that there is 1 orbital in s and that can hold up to 2 electrons, the p subshell has 3 orbitals that can hold up to 6 electrons, and the d subshell has 5 orbitals that hold up to 10 electrons. The 5p^4 orbital is not completely filled and using the periodic table you can deduce that Iodine is the answer to a.
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