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What is the de Broglie wavelength associated with (a) an electron moving with a speed of 5.4xx10^(6) m//s, and (b) a ball of mass 150 g travelling at 30.0 m//s? |
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Answer» Solution :(a) For the electron : Mass `m=9.11xx10^(-31)kg`. speed `V=5.4xx10^(6)m//s`. Then. Momentum `p=m v=9.11xx10^(-31)(kg)xx5.4xx10^(9)(m//s)` `p=4.92xx10^(-24)kgm//s` de BROGLIE wavelength, `lambda=h//p` `=(6.63xx10^(-34)Js)/(4.92xx10^(-24)kgm//s)` `lambda=0.135nm` (b) For the ball : Mass `m.=0.150 kg," speed v. "=30.0m//s` Then momentum `..=m.v.=0.150(kg)xx30.0(m//s)` `p.=4.50kg m//s` de Broglie wavelength `lambda.=h//p.` `=(6.63xx10^(-34)Js)/(4.50xxkgm//s)` `lambda.=1.47xx10^(-34)m` The de Broglie wavelength of electron is comparable with X-ray WAVELENGTHS. However, for the ball it is about `10^(-19)` times the size of the proton, quite beyond experimental measurement. |
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