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In the modern periodic table, which period contains 32 elements?

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Hint: The modern periodic table contains elements arranged in the order of increasing atomic number. As the atomic number increases the size of the atom increases and the atomic shell gets occupied. An atom consists of shells that hold subshells in which orbitals are present that have electrons. In a period the number of elements found is in accordance with the electrons filled in K, L, M and N shells.

Complete answer:
The modern periodic table is based on the law that physical and chemical properties of elements are the periodic function of their atomic numbers. So, the elements are arranged according to atomic numbers. The atomic numbers define the electronic configuration of atoms, through which the period and number of elements in a period can be determined.
For, 1st period, the n = 1 so the number of shells is 1 that means it has 2 elements as outer configuration is 1 s that can have 2 electrons.
For 2nd period n = 2, that means in the 2nd shell there can be 2s and 2p orbitals that can have a total 8 electrons, which means 8 elements.
Similarly as we move down the period we have in 3rd period 8 electrons, in 4th and 5th periods 18 each due to s, p, and d subshells having valence electrons.
Now, as period 6 involves 6s, 4f, 5d and 6p subshells in valence configuration, these subshells can have a total 32 electrons, which means there can be 32 elements in the period 6.
Also, in the 7th period the subshells of the valence configuration are 7s, 5f, 6d and 7p, that means a total of 32 electrons and 32 elements.
So, in the modern periodic table, the periods that contain 32 elements are 6th and 7th period.

Note:
The filling of shells define the elements in each period as K has 2, L-8, M- 18, N – 32, so the periods that fill these shells have a respective number of elements present in the periods. The filling of orbitals in the s, p, d and f subshells in the electronic configuration is in accordance with the Aufbau principle.