The de broglie relation and the wavelength of a particle just as light waves have particle behavior, a moving particle has a wave nature. the faster the particle is moving, the higher its kinetic energy and the shorter its wavelength. the wavelength, λ, of a particle of mass m, and moving at velocity v, is given by the de broglie relation λ=hmv where h=6.626×10−34 j⋅s is planck's constant. this formula applies to all objects, regardless of size, but the de broglie wavelength of macro objects is miniscule compared to their size, so we cannot observe their wave properties. in contrast, the wave properties of subatomic particles can be seen in such experiments as diffraction of electrons by a metal crystal.
part a the mass of an electron is 9.11×10−31 kg. if the de broglie wavelength for an electron in a hydrogen atom is 3.31×10−10 m, how fast is the electron moving relative to the speed of light? the speed of light is 3.00×108 m/s. express your answer numerically as a percent.
part b the mass of a golf ball is 45.9 g . if it leaves the tee with a speed of 63.0 m/s , what is its corresponding wavelength?

most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).

answer : (a) volume of the gas = 8.67 ×   l

                (b) second virial coefficient b = -1.21226 l/mole

solution :   given,     t = 300k

                                p = 20atm

                                z = 0.86

                                n = 8.2 mmoles = 8.2 × moles

                                r =   0.082 l atm/k/mol

        find,     (a) volume of gas   and (b) second virial coefficient b at 300k.

formula used :            

                          and            

(a)            

                    = \times 0.082\times 300}{20}[/tex]

                    = 8.67 ×   l

(b)      

                    = (0.00867-1) × 8.659

                    = - 8.5839 l/mole