31) Find the de Broglie wavelength associated with an alpha particle emitted with a kinetic energy of 1 MeV by the nucleus of an atom of radon.

32) Two slits are placed 2 mm apart and 300 cm from a screen. When light of 6000 A (angstroms) is used find the separation between the bright lines of the interference pattern in mm.

33) If the mean lifetime of the excited state of Cd 111 is T

_{1/2}

= 8 x 10

^{- 8}sec, find the

*half-width*of the excited state.

Questions 34 and 35:

The decay of a radioactive sample obeys the following relation:

N = N

_{o}exp (-lt)

where N is the amount of the sample at some time t, and N

_{o}is the amount of the sample at an initial time t

_{o}= 0.

34) Find the half -life of one of the atoms in the radioactive sample.

35) Find the

*mean lif*e of one of the atoms in the radioactive sample.

36) By

*what fraction*is the kinetic energy of a neutron (mass m1)

*decreased*in a head-on elastic collision with an atomic nucleus (mass m2) initially at rest?

37) If an HCl molecule has an inter-nuclear distance of 1.27 A and the atomic weight of a Cl atom is 36, find the

*moment of inertia*of the molecule about the center of mass.

38) Find the

*Lande g-factor*for an atom in the state 1D

_{3/2}.

39) Estimate the

*average binding energy*of a nucleon in the nucleus of an atom.

40) In the near infrared spectrum of carbon monoxide, there is an intense band at 2144 cm

^{-1}. Estimate from this the fundamental vibration frequency of CO.

41) Find the voltage induced in a coil with an inductance of 0.25 H (henries) when the current is decreased uniformly from 2 amperes to zero amperes in 1/16 sec.

42) Assuming the density of air to be constant near the Earth's surface, and the barometric pressure at sea level is 76 Hg, estimate the barometric pressure at an elevation of 200' above sea level.

43) A sphere of radius a has uniform charge density of q distributed within it. Find the total electrostatic energy of this system.

44) An oscillating circuit contains an inductance of 10 m h (micro-henries), a capacitor of 5 mf (micro-farad) and a capacitor of 25 mf, all in parallel. Find the natural frequency, f, of this circuit.

45) The relation between pressure and volume in an adiabatic expansion is:

pv

^{n}= k.

If the specific heat at constant pressure is c

_{p}and the specific heat at constant volume is c

_{v}, then n = ?

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