Question

# An early model for an atom considered it to have a positively charged point nucleus of charge Ze, surrounded by a uniform density of negative charge upto a radius R. The atom as a whole is neutral. The electric field at a distance r from the nucleus is (r<R).

A
Ze4πϵ0[1r2rR3]
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Ze4πϵ0[1r2rR2]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Ze4πϵ0[1R3rr2]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Ze4πϵ0[1R3+rr2]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A Ze4πϵ0[1r2−rR3]Charge on nucleus is =+Zetotal negative charge =−Ze(∵ atoms is electrical neutral)Negative charge density, ρ=chargevolume=−Ze43πR3i.e., ρ=−34ZeπR3...(i)Consider a Gaussian surface with radius rBy Gauss's theoremϕ=E(r)×4πr2=qε0....(ii)Charge enclosed by Gaussian surfaceq′=Ze+4πr33ρ=Ze−Zer3R3 [Using (i)]From (ii)E(r)=q′4πε0r2=Ze−Zer3R34πε0r2=Ze4πε0(1r2−rR3)

Suggest Corrections
2
Join BYJU'S Learning Program
Related Videos
Gauss' Law Application - Electric Field Due to a Sphere and Thin Shell
PHYSICS
Watch in App
Join BYJU'S Learning Program