JEE Advanced · Chemistry · 3. Periodic Table

The colour of the $X_{2}$ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to -

A Decrease $i n H O M O - L U M O$ gap down the group
B Decrease in $π^{*} - σ^{*}$ down the group
C The physical state of $X_{2}$ at room temperature changes from gas to solid down the group
D Decrease in ionization energy down the group

Verified Solution

Answer & Solution

Correct Answer

(B) Decrease in $π^{*} - σ^{*}$ down the group

Step-by-step Solution

Detailed explanation

Halogens are coloured due to HOMO-LUMO transition of electrons.

On moving down the group HOMO-LUMO energy gap decreases so transition of electrons become easier from

{Π^{*}}_{2 p_{x}}

{σ^{*}}_{2 p_{z}}

therefore colour intensify.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Match the statements of Column I with these in Column II.
[Note : Here $z$ takes values in the complex plane and $\operatorname{Im}(z)$ and $\operatorname{Re}(z)$ denote respectively, the imaginary part and the real part of $z$ ]

Column I	Column II
(A)The set of points $z$ satisfying $\|z-i\| z\|\|=\|z+i\| z\|\|$ is contained in or equal to	(p)an ellipse with eccentricity $4 / 5$
(B) The set of points $z$ satisfying $\|z+4\|+\|z-4\|=0$ is contained in or equal to	(q) the set of points $z$ satisfying $\operatorname{Im}(z)=0$
(C) If $\|w\|=2$, then the set of points $z=w-\frac{1}{w}$ is contained in or equal to	(r) the set of points $z$ satisfying $\|\operatorname{Im} z\| \leq 1$
(D) If $\|w\|=1$, then the set of points $z=w+\frac{1}{w}$ is contained in or equal to	(s) the set of points satisfying $\|\operatorname{Re} z\| \leq 2$
	(t) the set of points $z$ satisfying $\|z\| \leq 3$

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LIST-I contains compounds and LIST-II contains reactions

List - I	List - II
(I) $H _2 O _2$	(P) $Mg \left( HCO _3\right)_2+ Ca$ $(OH)_2 \rightarrow$
(II) $Mg ( OH )_2$	(Q) $BaO _2+ H _2 SO _4 \rightarrow$
(III) $BaCl _2$	(R) $Ca \left( OH _2\right) 2$ $+ MgCl _2 \rightarrow$
(IV) $CaCO _3$	(S) $BaO _2+ HCl \rightarrow$
	(T) $Ca \left( HCO _3\right)_2$ $+ Ca ( OH )_2$

Match each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct option

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Let $\mathbb{R}$ denote the set of all real numbers. For a real number $x$, let $[x]$ denote the greatest integer less than or equal to $x$. Let $n$ denote a natural number.
Match each entry in List-I to the correct entry in List-II and choose the correct option.

	LIST - I		LIST - II
(P)	The minimum value of $n$ for which the function $f(x)=\left[\frac{10 x^3-45 x^2+60 x+35}{n}\right]$ is continuous on the interval $[1,2]$,is	(1)	8
(Q)	The minimum value of $n$ for which $g(x)=\left(2 n^2-13 n-15\right)\left(x^3+3 x\right),x \in \mathbb{R}$,is an increasing function on $\mathbb{R}$,is	(2)	9
(R)	The smallest natural number $n$ which is greater than 5,such that $x=3$ is a point of local minima of $h(x)=\left(x^2-9\right)^{\mathrm{n}}\left(x^2+2 x+3\right)$,is	(3)	5
(S)	Number of $x_0 \in \mathbb{R}$ such that $l(x)=\sum_{k=0}^4\left(\sin \|x-k\|+\cos \left\|x-k+\frac{1}{2}\right\|\right),x \in \mathbb{R}$,is NOT differentiable at $x_0$,is	(4)	6
		(5)	10

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Column I	Column II
(A)The set of points \(z\) satisfying \(\|z-i\| z\|\|=\|z+i\| z\|\|\) is contained in or equal to	(p)an ellipse with eccentricity \(4 / 5\)
(B) The set of points \(z\) satisfying \(\|z+4\|+\|z-4\|=0\) is contained in or equal to	(q) the set of points \(z\) satisfying \(\operatorname{Im}(z)=0\)
(C) If \(\|w\|=2\), then the set of points \(z=w-\frac{1}{w}\) is contained in or equal to	(r) the set of points \(z\) satisfying \(\|\operatorname{Im} z\| \leq 1\)
(D) If \(\|w\|=1\), then the set of points \(z=w+\frac{1}{w}\) is contained in or equal to	(s) the set of points satisfying \(\|\operatorname{Re} z\| \leq 2\)
	(t) the set of points \(z\) satisfying \(\|z\| \leq 3\)

List - I	List - II
(I) \(H _2 O _2\)	(P) \(Mg \left( HCO _3\right)_2+ Ca\) \((OH)_2 \rightarrow\)
(II) \(Mg ( OH )_2\)	(Q) \(BaO _2+ H _2 SO _4 \rightarrow\)
(III) \(BaCl _2\)	(R) \(Ca \left( OH _2\right) 2\) \(+ MgCl _2 \rightarrow\)
(IV) \(CaCO _3\)	(S) \(BaO _2+ HCl \rightarrow\)
	(T) \(Ca \left( HCO _3\right)_2\) \(+ Ca ( OH )_2\)

	LIST - I		LIST - II
(P)	The minimum value of \(n\) for which the function \(f(x)=\left[\frac{10 x^3-45 x^2+60 x+35}{n}\right]\) is continuous on the interval \([1,2]\),is	(1)	8
(Q)	The minimum value of \(n\) for which \(g(x)=\left(2 n^2-13 n-15\right)\left(x^3+3 x\right),x \in \mathbb{R}\),is an increasing function on \(\mathbb{R}\),is	(2)	9
(R)	The smallest natural number \(n\) which is greater than 5,such that \(x=3\) is a point of local minima of \(h(x)=\left(x^2-9\right)^{\mathrm{n}}\left(x^2+2 x+3\right)\),is	(3)	5
(S)	Number of \(x_0 \in \mathbb{R}\) such that \(l(x)=\sum_{k=0}^4\left(\sin \|x-k\|+\cos \left\|x-k+\frac{1}{2}\right\|\right),x \in \mathbb{R}\),is NOT differentiable at \(x_0\),is	(4)	6
		(5)	10

The colour of the X2 molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to -

Step-by-step Solution

The colour of the $X_{2}$ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to -