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Calculate the velocity of electron in the first Bohr orbit of hydrogen atom. Given that Bohr radius = 0.529 Å, Planck's constant, h = 6.626 xx 10^(-34)Js, mass of electron = 9.11 xx 10^(-31) kg and 1J = 1kg m^(2) s^(-2). Also calculate the velocity of electron in third orbit of He^(+) ion |
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Answer» Solution :`mvr = (nh)/(2pi) or v = (nh)/(2pi mr) = ((1) (6.626 xx 10^(-34) Js))/(2 xx 3.14 xx (9.11 xx 10^(-31) KG) xx (0.529 xx 10^(-10)m))` But `1J = 1 kg m^(2) s^(-2)` Hence, `v = 2.189 xx 10^(6) ms^(-1)` For H-like particles, velocity of electron in nth ORBIT is given by `v_(n) = (Z)/(n) xx v_(0)` (`v_(0)`= velocity of electron in 1st orbit of H-atom) For `He^(+), Z = 2` `:. v_(3) = (2)/(3) xx 2.189 xx 10^(6) ms^(-1) = 1.459 xx 10^(6) ms^(-1)` |
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