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An electron is at a distance of 10 m fro...

An electron is at a distance of 10 m from a charge of 10c.Its total energy is `15.6xx10^(-10)` J.Its de-Broglie wavelength at this point is…….. .`(h=6.625xx10^(-34))`J.s ,`m_(e)=9.1xx10^(-31)kg, K=9xx10^(9)SI`

Text Solution

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Potential energy of an electron ,`U=-(kq(e))/(r )`
`therefore U=-(9xx10^(9)xx10xx1.6xx10^(-19))/(10)`
`therefore U=-14.4xx10^(-10)J`
Now total energy E=Kinetic energy K+potential energy U
`therefore`K=E-U
`=15.6xx10^(-10)+14.4xx10^(-10)`
`therefore K=30xx10^(-10)J`
But K`=(p^(2))/(2m_(e))`
`therefore p=sqrt(2km_(e))`
`lambda=(h)/(sqrt(2km_(e)))=(6.625xx10^(-34))/(sqrt(2xx30xx10^(-10)xx9.1xx10^(-31)))`
`therefore lambda=8.97xx10^(-15)m`
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