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The mass of an electron is 9.1 xx 10^...

The mass of an electron is `9.1 xx 10^(31) kg` if its K.E. Is `3.0 xx 10^(25) J` calculate its wavelength .

Text Solution

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Kinetic energy `(1)/(20 mv^(2) = k.e` `3.0 10^(25) J = (1)/(2) (9.1 xx 10^(31) kg) v^(2)`
`m=9.1 xx 10^(31) kg`
`K.E. = 3.0 xx 10^(25)`
`=sqrt(0.6593 xx 10^(6) kg m^(2) s^(2) kg^(-1))`
`=812 .0 ms^(-1)`
Calculation of wavelength `(lambda)`
According to de -Broglie
`h= 6.626 xx 10^(34) J s`
`lambda = (h)/( mv)`
`=6.626 xx 10^(34) kg m^(2) s^(-1)`
`=(6.626 xx 10^(34) kg m^(2) s^(-1))`
`(9.1 xx 10^(31 ) kg) (812 ms^(-1))`
`=8.967 xx 10^(7) m`
`=8967 xx 10 ^(9) m = 897 nm`
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