The energy needed to detach the electron of a hydrogen like ion in ground state is a system(a) what is the wavelength of the radiation emitted when the electron jumps from the first excited state to the ground state? (b) What is the radius of the orbit for this atom?
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A, B, C
(i) `E_(0) = - (I.E.)/(n^(2)) ` for Bohr 's hydrogen atom . ` Here I.L. = 4R :. E_(0) = (-4R)/(n^(2))` ` :. E_(2) - E_(1) = (-4R)/(2^(2)) - ((-(4R)/(1^(2))) = 3R ` ….(ii) ` E_(2) - E_(1) = = hv = (hc)/(lambda)` ….(iii) from (i) and(ii) ` (hc)/(lambda) = 3R` ` :. lambda = (hc)/(3R) = (6.6 xx 10^(-34) xx 3 xx 10^(8))/(2.2 xx 10 ^(-18) xx 3) = 300 Å` The nucleus of the first orbit Bohr's radius ofhydrogen atom `= 5 xx 10^(-11) m ` (given) `|E| = + 0.22 xx 10^(-17) Z^(*2) = 4R = 4 xx 2.2 xx 10^(-18)` :. r_(0) = (5 xx 10^(-11))/(Z) = ( (5 xx 10^(-11))/(2) = 2.5 xx 10^(-11)m`
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