An electron in a hydrogen atom in the ground state absorbs energy equal to 1.5 time the minimum energy required to remove the electron from the hydrogen atom. Calculate the wavelength of the electron emitted.

An electron in a hydrogen atom in the ground state absorbs energy equa

1.	An electron in a hydrogen atom in the ground state absorbs energy equal to 1.5 time the minimum energy required to remove the electron from the hydrogen atom. Calculate the wavelength of the electron emitted.
Answer» Solution :Energy required to remove electron from ground state of H-atom = 13.6 eV `:.` Energy absorbed by the electron `= 1.5 xx 13.6 eV = 20.4 eV` After the REMOVAL of electron from the atom, extra energy which is converted into kinetic energy `= 20.4 - 13.6 = 6.8 eV` Thus, `(1)/(2) mv^(2) = 6.8 xx 1.602 xx 10^(-19)J` or `v = sqrt((2 xx 6.8 xx 1.602 xx 10^(-19))/(9.11 xx 10^(-31))) = sqrt(2.4 xx 10^(12)) = 1.55 xx 10^(6) MS^(-1)` `lamda = (h)/(mv) = (6.63 xx 10^(-34) KG m^(2) s^(-1))/((9.11 xx 10^(-31) kg) (1.55 xx 10^(6) ms^(-1))) = 4.70 xx 10^(-10) m`