The correct orders among the following are:
[A.] Atomic radius : \(B<Al<Ga<In<Tl\)
[B.] Electronegativity : \(Al<Ga<In<Tl<B\)
[C.] Density : \(Tl<In<Ga<Al<B\)
[D.] 1st Ionisation Energy :
In\(<Al<Ga<Tl<B\)
Choose the correct answer from the options given below :
Let's analyze the trends in Group 13 elements (Boron family) for the given properties: B, Al, Ga, In, Tl. Atomic Radius: Generally, atomic radius increases down a group due to the addition of new electron shells.
However, there's an anomaly due to poor shielding by the d-electrons in Ga.
The correct order is B<Al<Ga<In<Tl. Order A: B<Al<Ga<In<Tl (Correct)
Electronegativity: Electronegativity generally decreases down a group due to increasing atomic size and shielding. However, due to the poor shielding by d-electrons in Ga and In, their electronegativities are slightly higher than expected.
The general trend is B>Al>Ga \approx In>Tl. The given order is Al<Ga<In<Tl<B. Order B: Al<Ga<In<Tl<B (Correct) Density: Density generally increases down a group due to increasing atomic mass. However, the volume also plays a role.
The order is B<Al<Ga<In<Tl. The given order is Tl<In<Ga<Al<B. Order C: Tl<In<Ga<Al<B (Incorrect, the density of Al is less than Ga) First Ionisation Energy: Ionisation energy generally decreases down a group due to increasing atomic size and shielding. However, there are irregularities due to the electronic configurations.
The correct order is B>Al<Ga<Tl<In. The given order is In<Al<Ga<Tl<B. Order D: In<Al<Ga<Tl<B (Correct) From the analysis: Order A (Atomic radius) is correct. Order B (Electronegativity) is correct. Order C (Density) is incorrect. Order D (1st Ionisation Energy) is correct.
The correct orders are B and D. Therefore, the correct option is (1).
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: