Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is:
Halogens are the group 17 elements of the periodic table. The term ‘halogen’ means ‘salt-producing’, hence the name halogens as they possess the tendency to form salts after reacting to metals. It generally has five elements:
These are all naturally occurring halogens but Tennessine (Ts) is an artificially created halogen.
Halogens are highly reactive elements and are highly electronegative. They have a high tendency to react with metals to form salts. They are also known as Group 17 elements. They have 7 electrons in their outer shell with a configuration of (ns2 np5). Fluorine being the first halogen in group 17, is highly reactive. Astatine is a halogen because of its resemblance with iodine despite it being radioactive.
The general electronic configuration for group 17 elements is ns2np5. This configuration clearly shows that they have 7 electrons in their valence shell. They require one more electron to complete their octet and achieve noble gas configuration.
