Answer:
r = 0.303m
 = 30.3cm
Explanation:
Given that,
The number of electrons transferred from one sphere to the other,  
n  =
1
×10
¹³e
le
c
t
r
o
n
s
The electrostatic potential energy between the spheres,  
U
=
−
0.061
J
The charge on an electron,  
q
=
−
1.6
×
10
⁻¹⁹C
The coulomb constant,  
K
=
8.98755
×
10
⁹
N
⋅
m
²
/
C
2²
Due to the transfer of electrons, both spheres become equally and oppositely.
The charge gained by the sphere due to the excess of the electron is:  
q
₁ =
n
q
    =
1
×10
¹³ *  −
1.6
×
10
⁻¹⁹ 
    = -1.6  × 10⁻⁶C
The charge left on the first sphere is =
q
₂ = -q₁ = 1.6  × 10⁻⁶C
The electric potential energy between two point charges is given by the following equation:
U
=
K
q
₁q
₂/r
q
₁ and  q
₂ are the two charges.
r  is the distance between the charge and the point.
K  =  8.98755  ×  10
⁹
N
⋅
m
²
/
C
²
 we have:
-0.061 =  (8.98755  ×  10
⁹ * (-1.6  × 10⁻⁶)²) / r
r = (18.41 ×  10
⁻³) / 0.061
r = 0.303m
 = 30.3cm