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What is the de Broglie wavelength relate...

What is the de Broglie wavelength related to an electron of energy 100 eV ? (Given, mass of electron, `m = 9.1 xx 10^(-31) kg, " " e = 1.6 xx 10^(-19) C and h = 6.63 xx 10^(-34) J.s`)

Text Solution

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Let the velocity of electron be v. Its kinetic energy,
`(1)/(2) mv^(2) = E or, m^(2) v^(2) = 2mE`
or, `mv = sqrt(2mE)`
`:.` de Broglie wavelength related with the electron,
`lamda = (h)/(mv) = (h)/(sqrt(2mE))`
`= (6.63 xx 10^(-34))/(sqrt(2 xx 9.1 xx 10^(-31) xx 100 xx 1.6 xx 10^(-19)))`
`= 1.23 xx 10^(-10) m = 1.23 Å`
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