Saved Bookmarks
| 1. |
An earlymodel for an atom consideredit to have a positivelychargedpointnucleasof charge Ze,surrounded by a unifromdensity of negative chargeupto a radius R. The atomas a wholeis neutral. For this model, What is the electricfieldat a distancer from the nucleas ? |
|
Answer» Solution :The charge distributionfor this model of atomis shown in Fig. Chargeon nucleas `= +Ze` , As atom is neutral, total NEGATIVE charge `= -Ze` `:.` Negativechargedensity, `p = (charg e)/(Volume)`  `p = (-Ze)/((4)/(3) 4pi R^(3)) = (-3Ze)/(4pi R^(3))`...(i) IMAGINE a GAUSSIAN surface- which is a spherical surface of radius r withcenterat thenucleaus (not shown). According to Gauss's theorem in electrostatics. `phi = E(r)xx4pi r^(2) = (q)/(in_(0))` ...(ii) (i) When point `P_(1)` is outside, i.e., `r gt R, q = Ze - Ze = 0 :. E(r) = 0`. (ii) When point `P_(2)` is inside, i.e., `r gt R`, Chargeenclosed by Gaussain surface. `q' = Ze + (4pi r^(3))/(3) p = Ze - Ze (r^(3))/(R^(3))` ...using (i) From(ii), `E (r)= (q')/(4pi in_(0) r^(2)) = (Ze-Ze r^(3) // R^(3))/(4pi in_(0) r^(2))` `= (Ze)/(4pi in_(0)) ((1)/(r^(2)) - (r)/(R^(3)))` |
|