how to find no of unpaired electrons in z=64

To find the number of unpaired electrons in an atom with atomic number Z=64, we need to determine the electron configuration of the atom.

Step 1: Determine the electron configuration of the atom. The atomic number of an element tells us the number of electrons in a neutral atom. For Z=64, the element is Gadolinium (Gd). The electron configuration of Gd can be determined by referring to the periodic table or using the Aufbau principle.

The electron configuration of Gd is: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f⁷ 5d¹ 6p⁶.

Step 2: Determine the number of valence electrons. Valence electrons are the electrons in the outermost energy level of an atom. In the case of Gd, the outermost energy level is the 6s² 4f⁷ 5d¹ 6p⁶ configuration. Counting the electrons in this configuration, we find that Gd has 9 valence electrons.

Step 3: Determine the number of paired electrons. Paired electrons are electrons that are paired up in the same orbital. In the case of Gd, the 4f sublevel has 7 electrons, which means that 3 pairs of electrons are paired up.

Step 4: Determine the number of unpaired electrons. To find the number of unpaired electrons, subtract the number of paired electrons from the number of valence electrons. In the case of Gd, we have 9 valence electrons and 3 pairs of paired electrons. Therefore, the number of unpaired electrons in Gd is 9 - 3 = 6.

So, the number of unpaired electrons in an atom with Z=64 (Gadolinium) is 6.