C HAPTER . (a) No different from (b) Thomson’s model; Rutherford’s model (c) Rutherford’s model (d) Thomson’s model; Rutherford’s model (e) Both the models . The nucleus of a hydrogen atom is a proton. The mass of it is .
× – kg, whereas the mass of an incident ( -particle is . × – kg. Because the scattering particle is more massive than the target nuclei (proton), the ( -particle won’t bounce back in even in a head-on collision. It is similar to a football colliding with a tenis ball at rest.
Thus, there would be no large-angle scattering. . nm. .
Lyman series: nm and nm; Balmer series: nm. . . × .
(a) About the same. (b) Much less. (c) It suggests that the scattering is predominantly due to a single collision, because the chance of a single collision increases linearly with the number of target atoms, and hence linearly with thickness. (d) In Thomson’s model, a single collision causes very little deflection.
The observed average scattering angle can be explained only by considering multiple scattering. So it is wrong to ignore multiple scattering in Thomson’s model. In Rutherford’s model, most of the scattering comes through a single collision and multiple scattering effects can be ignored as a first approximation. .
The first orbit Bohr’s model has a radius a given by a = ( / ) h m e e . If we consider the atom bound by the gravitational force ( Gm p m e /r ), we should replace ( e / ) by Gm p m e . That is, the radius of the first Bohr orbit is given by a h Gm m G p e ( / ) . m.
This is much greater than the estimated size of the whole universe! . me h ( ) ( / ) ( ) me h n n ( ) ( ) ( / ) ( ) For large n , me h ( / )