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- Atomic numbers: 58 to 71 (Ce to Lu)
- Period: Sixth (belong to period 6)
- Sub-level being filled: 4f
- Total: 14 elements
The dimensional formula of angular momentum is:
Angular momentum $L = I\omega = mvr$ (for a particle)
$[L] = [m][v][r] = M \cdot LT^{-1} \cdot L = ML^2T^{-1}$
This is the same as the dimension of Planck's constant $h$, which makes sense since $E = h\nu$ and angular momentum appears in quantum mechanics through $\hbar = h/2\pi$.
A body starts from rest and moves under constant acceleration for 20 s. It covers distance $S_1$ in the first 10 s and $S_2$ in the next 10 s. Then $S_2$ equals:
Using $s = \dfrac{1}{2}at^2$ (from rest):
$S_1 = \dfrac{1}{2}a(10)^2 = 50a$
Total in 20 s: $S_{\text{total}} = \dfrac{1}{2}a(20)^2 = 200a$
$S_2 = 200a - 50a = 150a = 3 \times 50a = \mathbf{3S_1}$
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