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Question: In a diatomic molecule the bond distance is \(1\times {{10}^{-8}}cm\). Its dipole moment is 1.2D. Wh...

In a diatomic molecule the bond distance is 1×10−8cm1\times {{10}^{-8}}cm. Its dipole moment is 1.2D. What is the fractional electric charge on the atom?
a) 0.50
b) 1.2×10−101.2\times {{10}^{-10}}
c) 0.25
d) 1.2

Explanation

Solution

The correct answer to this question includes the formula of dipole moment which is given by, Dipole moment = electronic charge×\times its distance (meaning bond length) where Debye is written in terms of esu.cm.

Complete answer:
According to some basic concepts of chemistry, let us write the dipole moment in terms of its esu.cm as per the data given as,
Dipole moment = q×\times 1×10−8cm1\times {{10}^{-8}}cm
Where, q = electronic charge and also bond distance according to the question is 1×10−8cm1\times {{10}^{-8}}cm
Substituting the values, we get
1.2D = q×\times 1×10−8cm1\times {{10}^{-8}}cm
Here, Debye in terms of cm is given as, 1D =10−18cm{{10}^{-18}}cm.
Therefore, the expression becomes
q = 1.2×10−181×10−8\dfrac{1.2\times {{10}^{-18}}}{1\times {{10}^{-8}}}
By solving this above equation we get,
q = 1.2×10−10esu1.2\times {{10}^{-10}}esu
Now, we have to find the fraction of electric charge present on the atom.
For this, first consider the electronic charge on each atom in terms of esu. This is given by,
e =4.8×10−10esu4.8\times {{10}^{-10}}esu
This implies that we have to calculate fraction of charge per atom which is given by
fraction of charge per atom = 1.2×10−104.8×10−10\dfrac{1.2\times {{10}^{-10}}}{4.8\times {{10}^{-10}}}
Therefore, fraction of charge per atom = 0.25

Thus, the correct answer is option c) 0.25.

Additional information:
esu is a notation given for the unit for electric current which is abbreviated as electrostatic unit of charge per second. This is used when the electric charge measurement is to be done in minor quantities.

Note:
The option in the multiple choices also contains the value 1.2×10−101.2\times {{10}^{-10}}. Note that the question is read carefully and do not assume that this calculated answer is the total charge on the atom as the actual answer. Reading the question thoroughly is mandatory.