If the equation of state for a gas with internal energy U is pV = $$\frac{1}{3}$$U, then the equation for an adiabatic process is

All vibrations producing a change in the electric dipole moment of a molecule yield

A. Raman spectra

B. Infrared spectra

C. Ultra-violet spectra

D. X-ray spectra

A piece of paraffin is placed in a uniform magnetic field H₀. The sample contains hydrogen nuclei of mass m_p, which interact only with external magnetic field. An additional oscillating magnetic field is applied to observe resonance absorption. If g₁ is the g-factor of the hydrogen nucleus, the frequency at which resonance absorption takes place, is given by

A. $$\frac{{3{g_1}e{H_0}}}{{2\pi {m_p}}}$$

B. $$\frac{{3{g_1}e{H_0}}}{{4\pi {m_p}}}$$

C. $$\frac{{{g_1}e{H_0}}}{{2\pi {m_p}}}$$

D. $$\frac{{{g_1}e{H_0}}}{{4\pi {m_p}}}$$

Consider the following statements about molecular spectra:
P. CH₄ does not give pure rotational Raman lines
Q. SF₆ could be studied by rotational Raman spectroscopy
R. N₂ shows infrared absorption spectrum
S. CH₃CH₃ shows vibrational Raman and infrared absorption lines
T. H₂O₂ shows pure rotational spectrum
Choose the right combination of correct statements.

A. P and Q

B. P, R and T

C. P, S and T

D. Q and R

The hyperfine structure of Na(3²P_3/2) with nuclear $$l$$ = 3/2 has

A. 1 state

B. 2 states

C. 3 states

D. 4 states