GATE CY 2018 Paper 1 — page 20

Questions 58–60 of 65. Imported answers require review unless explicitly marked reviewed.

In a molecule XY, let

and

denote normalized atomic orbitals of atoms X and Y, respectively. A normalized molecular orbital of XY is given by

. The value of the overlap integral of

and

is ________________. (Up to two decimal places)

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The absorption maxima of two dyes X and Y are 520 and 460 nm, respectively. The absorbance data of these dyes measured in a 1 cm path length cell are given in the table below.

Dye solution	Absorbance at 460 nm	Absorbance at 520 nm
X (9 mM)	0.144	0.765
Y (12 mM)	0.912	0.168
Mixture of X and Y	0.700	0.680

The concentration of Y in the mixture is ________ mM. (Up to two decimal places)

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The π electrons in benzene can be modeled as particles in a ring that follow Pauli’s exclusion principle. Given that the radius of benzene is 1.4 Å, the longest wavelength of light that is absorbed during an electronic transition in benzene is __________ nm. (Up to one decimal place. Use mₑ = 9.1×10⁻³¹ kg, h = 6.6×10⁻³⁴ J s, c = 3.0×10⁸ m s⁻¹)

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2018 · Paper 1

Question 48

Question 49

Question 50