At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rmsspeed of a helium gas atom at `-20 ^@C` ? (atomic mass of Ar = 39.9 u, of He = 4.0 u).

What is the de-Broglie wavelengths of a nitrogen molecule in air at 300 K? Assume that the molecule is moving with the root-mean-square speed of molecules at this temperature. (Atomic mass of nitrogen = 14.0076 u).

The molecules of a given mass of a gas have root mean squar speeds of 100 ms^-1 at 27^@C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the as at 127^@C and 2.0 atmospheric pressure?

A sample of paramagnetic salt contains 2.0 xx 10^24 atomic dipoles each of dipole moment 1.5 xx 10^-23 JT^-1 . The sample is placed under a homogeneous magnetic field of 0.64 T, and cooled to a temperature of 4.2 K. The degree of magnetic saturation achieved is equal to 15%. What is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8 K? (Assume Curie’s law)

Three conductivity cells A, B and C containing solutions of zinc sulphate, silver nitrate and copper sulphate respectively are connected in series. A steady current of 1.5 amperes is passed through them until 1.45 g of silver is deposited at the cathode of cell B. How long did the current flow ? What mass of copper and what mass of zinc got deposited in their respective cells ? (Atomic mass : Zn = 65.4 u, Ag = 108 u, Cu = 63.5 u)

A vessel contains two non-reactive gases, neon (monatomic) and oxygen (diatomic). The ratio of their partial pressures is 3.2. Estimate the ration of (i) number of molecules and (ii) mass density of neon and oxyge in the vessel. Atomic mass of Ne- 20.2 u, molecular mass of O_2 = 32.0 u.

What mass of zinc can be produced by the electrolysis of zinc sulphate solution when a current of 1.5 amperes is passed for 15 mnutes ? Atomic mass of zinc =65.4 a.m.u.

In the chemical analysis of a rock the mass ratio of two radioactive isotopes is found to be 100:1. The mean lives of the two isotopes are 4xx10^9 years and 2xx10^9 years, respectively. If it is assumed that at the time of formation the atoms of both the isotopes were in equal propotional, calculate the age of the rock. Ratio of the atomic weights of the two isotopes is 1.02:1.

Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature 17 ^@C . Take the radius of a nitrogen molecule to be roughly 1.0overset@ A . Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of N_2 = 28.0 u).

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules ? Is the root mean square speed of molecules the same in the three cases? If not, in which case is u_rms the largest ?