wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Consider the following very rough model of a beryllium atom. The nucleus has four protons and four neutrons confined to a small volume of radius 10−15 m. The two 1 s electrons make a spherical charge cloud at an average distance of 1⋅3 ×10−11 m from the nucleus, whereas the two 2 s electrons make another spherical cloud at an average distance of 5⋅2 × 10−11 m from the nucleus. Find three electric fields at (a) a point just inside the 1 s cloud and (b) a point just inside the 2 s cloud.

Open in App
Solution

(a)

Let us consider the three surfaces as three concentric spheres A, B and C.
Let us take q = 1.6×10-19 C .

Sphere A is the nucleus; so, the charge on sphere A, q1 = 4q
Sphere B is the sphere enclosing the nucleus and the 2 1s electrons; so charge on this sphere, q2 = 4q- 2q = 2q
Sphere C is the sphere enclosing the nucleus and the 4 electrons of Be; so, the charge enclosed by this sphere,q3 = 4q-4q = 0
Radius of sphere A, r1 = 10-15 m
Radius of sphere B, r2 = 1.3×10-11m
Radius of sphere C, r3 = 5.2×10-11 m
As the point 'P' is just inside the spherical cloud 1s, its distance from the centre
x=1.3×10-11 m
Electric field,
E=q4π 0 x2
Here, the charge enclosed is due to the charge of the 4 protons inside the nucleus. So,

E=4×1.6×10-194×3.14×8.85×10-12×1.3×10-112E=3.4×1013 N/C


(b)

For a point just inside the 2s cloud, the total charge enclosed will be due to the 4 protons and 2 electrons. Charge enclosed,

qen=2q =2×1.6×10-19 C

Hence, electric field,

E=qen4π 0 x2
x = 5⋅2 × 10−11 m
E=2×1.6×10-194×3.14×8.85×10-12×5.2×10-112E=1.065×1012 N/C

Thus, E=1.1×1012 N/C

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Discovery of Electron and Its Charge
CHEMISTRY
Watch in App
Join BYJU'S Learning Program
CrossIcon