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(a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels. |
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Answer» Solution : (a) As per Bohr.s model speed of electron is given by `v_(N) = (e^(2))/(2 in_(0) n H) ` . where `e = 1.6 xx 10^(-19) C, epsi_(0) 8.85 xx 10^(-12)C^(2) N^(-1) m^(-2) and h = 6.63 xx 10^(-34) JS` `therefore"" v_(1) = (e^(2))/(2 in_(0) (1)h) = ((1.6 xx 10^(-19))^(2))/(2xx8.85 xx 10^(-12) xx 6.63 xx 10^(-34)) = 2.18 xx 10^(6) m s^(-1)` ` v_(2) = (v_(1))/(2) = 1.09 xx 10^(6) m s^(-1) and v_(3) = (v_(1))/(3) = 7.27 xx 10^(5) ms^(-1)` (B)Orbital period` T = (2pi r_(n))/(v_(n))= (2pi xx ((in_(0) n^(2) h^(2))/(pi m e^(2))))/(((e^(2))/(2 in_(0) n h))) = (4 in_(0)^(2) n^(3) h^(3))/(m e^(4))` `therefore"" T_(1) = (4 xx (8.85 xx 10^(-12)) xx (1)^(2) xx (6.63 xx 10^(-34))^(3))/((9.1 xx 10^(-31)) xx (1.6 xx 10^(-19))^(4)) = 1.52 xx 10^(-16)s` `T_(2) = T_(1) xx(2)^(3) = 1.52 xx 10^(-16) xx 8 = 1.22 xx 10^(-5)` and `T_(3) = T_(1) xx (3)^(3)= 1.52 xx 10^(-16) xx 27=4.11 xx 10^(-15)s` |
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