"537949-6-1P The relation between de Broglie wave length ( ? ) and momentum ( p ) of a particle isgiven byh ? ?p And the kinetic energy of the particle(E ) is related to it’s momentum ( p ) as andvelocity(v),2 p E ?2m p ? 2mE p?? m v1 2 E ? mv Now if an object moves with a velocity v then kinetic energy is 2 5 And, if an object is at temperature T then kinetic energy is E ? KT as oxygen is a di2 atomic gas.?19 (a) Put the electron’s given kinetic energy as 3eV?? 3 10 Joule in the equation of?31 p and mass of the electron m=9.1 ?10 kg?? 31 19 p ? 2 ?9.1 ?10 ?3 ?10 ?50 ?? 87.36 10?25 ? 9.34 ?10 kg ?m ? Now find de Broglie wave length by putting the value of p in the equation of h ? ? p ?34 6.626 ?10 ??25 9.34 ?10 ?9 ?? 0.709 10 ?10 ?? 7.0 10 m 6?? 19 13 (b) Put the proton’s kinetic energy as 7MeV ? 7 ?10 ?10 Joule ? 7 ?10 Joule and?27 proton’s mass m=1.67 ?10 kg in the equation of p?? 27 13 p ? 2 ?1.67 ?10 ?7 ?10 ?40 ?? 35.84 10?20 ? 6 ?10 kg ?m ? Now find de Broglie wave length by putting the value of p in the equation of h ? ? p ?34 6.626 ?10 ? ?20 6 ?10 ?14 ?? 1.104 10 ?15 ?? 11 10 m (c) Put the speed 200 m/s in the energy equation and he masss of the buckyball as m ?24 ?? 1.19 10 kg 1 2 E ? mv 2 1 ?24 2 ? ?1.19 ?10 ?(200)2 ?20 ?? 2.38 10 JouleTherefore,?? 24 20 p ? 2 ?1.19 ?10 ? 2.38 ?10 ?44 ?? 5.664 10?22 ? 2.38 ?10 kg ?m h Now, put p in the equation of ? ?p h ? ? p ?34 6.626 ?10 ??22 2.38 ?10 ?12 ?? 2.78 10 m (d) Put T= 300K at the energy equation relating T5 E ? KT 2 5 ?23 ? ?1.38 ?102 ?23 ?? 3.5 10 Joule Now put E in equation of p ?? 26 23 p ? 2 ? 2.656 ?10 ?3.5 ?10 ?50 ?? 185.92 10?25 ?13.6 ?10 kg ?m h Put p in the equation ? ?p h ? ? p ?34 6.626 ?10 ??25 13.6 ?10 ?10 ?? 4.8 10 m (e) For a rain drop take mass m= 1 mg and velocity v= 1cm/s. Put those to getmomentum as p?? m v ?? 62 ?1 ?10 kg ?10 m /s ?8 ?1 ?10 kg ?m /s Now, put p in equation of ?h ? ? p ?34 6.626 ?10 ??8 1 ?10 ?26 ?? 6.626 10 m (f) For yourself walking in the class put mass m= 100 kg and velocity v= 1m/s in themomentum equationp?? m v ?? 100kg 1m /s ?? 100kg m /s Now, put p in equation of ?h ? ? p ?34 6.626 ?10 ?100 ?36 ?? 6.626 10 mAs, you can see the wavelengths for the problem (e) and (f) are very small. So thequantum effect will be significant for the first four cases only. "