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The electron of H-atom in ground state a...

The electron of H-atom in ground state absorbs energy equal to 1.5 times the minimum energy, required to remove the electron from the hydrogen atom. Calculate the wavelength of the electron emitted. [mass of electron`=9.11xx10^(-31)kg`].

Text Solution

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Energy required to remove an electron from the round state of H-atom=13.6 eV. Therefore, energy absorbed by the electron of H-atom`=1.5xx13.6eV=20.4eV`
`therefore`Residual energy after removal of the electron
`=(20.4-13.6)eV=6.8eV=6.8xx1.602xx10^(-19)J`
This residual energy is converted into kinetic energy.
`therefore (1)/(2)mv^(2)=6.8xx1.602xx10^(-19)`
This residual energy is converted into kinetic energy.
`therefore (1)/(2)mv^(2)=6.8xx1.602xx10^(-19)`
`therefore v=sqrt((6.8xx1.602xx10^(-19))/(9.11xx10^(-31)))=1.546xx10^(6)m*s^(-1)`
`lamda=(h)/(mv)=(6.626xx10^(-34)kg*m^(2)*s^(-1))/((9.11xx10^(-31)kg)xx(1.546xx10^(6)m*s^(-1)))`
`=4.70xx10^(-10)m`
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