Introduction:
The NaCt crystal is an ionic crystal with a face-centered cubic structure. It is made up of positively charged sodium ions (Na+) and negatively charged chloride ions (Ct-). When the crystal is doped with 10° mol% of BaCh, it means that 10% of the sodium ions are replaced by barium ions (Ba2+) and 10% of the chloride ions are replaced by chalcogenide ions (Ch-).

Cationic vacancies:
Cationic vacancies are the vacant spaces in the crystal lattice that are left behind when some of the cations are replaced by other cations. In this case, when 10% of the sodium ions are replaced by barium ions, there will be cationic vacancies in the crystal lattice. Similarly, when 10% of the chloride ions are replaced by chalcogenide ions, there will be anion vacancies in the crystal lattice.

Number of cationic vacancies:
To determine the number of cationic vacancies in 1 mole of NaCt crystal, we need to use the following formula:

Number of cationic vacancies = (x / 100) * N

where x is the percentage of cations that are replaced, N is Avogadro's number (6.022 x 10^23), and the result is rounded to the nearest integer.

Using this formula, we can calculate the number of cationic vacancies in 1 mole of NaCt crystal as follows:

Number of sodium ions in 1 mole of NaCt crystal = 6.022 x 10^23
Number of barium ions doped in 1 mole of NaCt crystal = (10 / 100) * 6.022 x 10^23 = 6.022 x 10^22
Number of cationic vacancies = (6.022 x 10^22 / 6.022 x 10^23) * 6.022 x 10^23 = 6.022 x 10^22

Therefore, there will be 6.022 x 10^22 cationic vacancies in 1 mole of NaCt crystal when it is doped with 10° mol% of BaCh.