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What is the de Broglie wavelength associ...

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 ?

Text Solution

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For the electron:
Mass `m=9.11xx10^(-31)kg`, speed `v=5.4xx10^(6)m//s`.
Then, momentum `p=m=9.11xx10^(-31)(kg) xx 5.4xx10^(6)(m//s)`
`p=4.92xx10^(-24)kg m//s`
de Broglie wavelength, `lambda=h//p=(6.63xx10^(-34)Js)/(4.92xx10^(-24)kg m//s)=0.135nm`
For the ball :
Mass `m.=0.150 kg`, speed `v.=30.0 m//s`.
Then momentum `p.=m. v.=0.150(kg) xx 30.0(m//s)`.
`p.=4.50 kg m//s`
de Broglie wavelength `lambda.=h//p.=(6.63xx10^(-14)Js)/(4.50kg m//s)=1.47xx10^(-34)m`
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