To find the approximate separation of the centers of charges in the water molecule, we need to consider the work done in rotating the dipole in an electric field. The work done
W to rotate a dipole of moment
by an angle
θ in an electric field
is given by:
W=pE‌cos(θ)−pE‌cos(0)For a rotation by
180∘,θ=180∘, and
cos(180∘)=−1 :
W=pE‌cos(180∘)−pE‌cos(0) Since
cos(0)=1, the above equation simplifies to:
‌W=pE(−1)−pE(1)‌W=−pE−pE‌W=−2pE Given that the work done is:
5×10−25JAnd the electric field strength is:
E=2.5×104N∕CWe can find the dipole moment,
p :
5×10−25=−2p(2.5×104)Solving for
p :
‌5×10−25=−5×104p‌p=‌‌p=−1×10−29Cm Since the dipole moment
p is given by the product of the charge
q on the water molecule and the separation
d of the charges, we have:
p=qdFor a water molecule, the charge of each center (hydrogen or oxygen) can be approximated to the elementary charge
e (since a water molecule is neutral overall, but the centers have polarity):
q=1.6×10−19CTherefore, we can solve for the separation
d :
‌d=‌‌d=‌‌d=‌×10−10‌d≈0.625×10−10mSo, the approximate separation of the centers of charges is:
0.625×10−10mHence, the correct option is:
Option B:
0.625×10−10m