The total spin quantum number S of an atom is half the number of unpaired electrons. The magnitude of the total spin angular momentum is sqrtS(S+1) hbar. For a ground-state chromium atom, find this magnitude in units of hbar, to two decimal places.

JEE Main levelNumerical answerDifficulty 2 of 3as206

The total spin quantum number $S$ of an atom is half the number of unpaired electrons. The magnitude of the total spin angular momentum is $S (S + 1) ℏ$ . For a ground-state chromium atom, find this magnitude in units of $ℏ$ , to two decimal places.

Numerical answer type, answer in hbar, tolerance 0.02.

Cr is

3 d^{5} 4 s^{1}

with 6 unpaired electrons, so

S = 3

. Magnitude

= 3 \times 4 = 12 = 3.46 ℏ