Molecular Spectroscopy Report No. 1 Due: March 18, 2015 Wednesday

Molecular Spectroscopy Report No. 1

Due: March 18, 2015 Wednesday

You can get the atomic mass of elements from the reference books available in the library. Do not take average atomic mass of elements because isotopes should be treated separately.

Problem 1) The resolving power R of any dispersing element, such as a prism, is given by:

R=λ/dλ

Where λ is the wavelength and dλ is the resolution. Calculate the resolving power at a wavelength of 405.643 nm and a resolution of 0.94Å. What is the resolution at a wavelength of 750 nm?

Problem 2) Two lines in the emission spectrum of sodium (Na) appear at wavelengths of 16956.2 and 16973.4 cm^-1. What is the minimum value of the resolving power of a prism or diffraction grating necessary to resolve these two lines?

Problem 3) A beam of polychromatic radiation is passing through the grating, it will be fanned out into a series of spectra located symmetrically on each side of the normal to grating, in which the wavelength depends on the n number of the grating equation. Calculate the wavelength of radiation corresponding to n up to 5 from a grating with 2000 lines per cm and deflection angle of 6.00^o using the grating equation nλ=dsinθ.

Problem 4) An aqueous solution of iron (IV) nitrate appears red when viewed in white light. What colors is being absorbed by the solution?

Problem 5) How would you expect widening of the slits in a spectrometer to affect its resolution and its sensitivity?

Problem 6) Sketch the curve you would expect from Fourier transformation of a sine wave.

Problem 7) The moment of inertia of the NH radical is 1.68x10^-40 g cm². At what frequency would you expect to detect the transition J= 2 to J=3?

Problem 8) In the far-infrared spectrum of HBr, there is a series of lines having a separation of 16.94 cm^-1. Calculate the moment of inertia and the internuclear separation of HBr from this datum.

Problem 9) In the microwave spectrum of ¹²C¹⁶O, the J = 0 → 1 rotational transition has been measured at 115,271.204 MHz. Calculate the moment of inertia (in units of amuŲ) and the internuclear separation of CO.

Problem 10) In the far-infrared spectrum of HCl is a series of lines having a separation of 21.18 cm^-1. (a) Calculate from this moment of inertia and bond length for the principal isotopic species, ¹H³⁵Cl. (b) How would the spacing and intensity of the corresponding lines of the ¹H³⁷Cl isotope compare with those of ¹H³⁵Cl?

Problem 11) If we were suddenly to multiply the dimensions of a molecules, HCl, for example, by a factor of 100 (without changing its mass or electric properties), how would this affect its spectrum in the infrared and microwave regions?

Problem 12) The N3H molecule is found to have the principal moments of inertia IA = 1.3759x10^-40 g cm², IB = 69.38x10^-40 g cm², and IC = 70.75x10^-40 g cm². Is the molecule linear? Can it have a threefold axis? Is it planar?

Problem 13) Which of the following molecules may show a pure rotational microwave spectrum: (a) H2O, (b) H2O2, (c) NH3, (d) N2O?

Problem 14) Classify the following molecules in terms of symmetry.

(a) SF6 (b) C6H6 (c) NH3 (d) CH3F (e) H2CO (f) CF4 (g) C2H4

Problem 15) Water vapor molecule shows very complicate rotational spectrum over wide range which interrupts the astronomical observation of the universe by telescope on earth. Define three rotational axes and compare the size of moments of inertia about the axis. Explain why the spectrum shows so complicate structure.

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