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Calculate the induced dipole moment per unit volume of helium gas placed in an electric field of 6 \times 10^{5} \mathrm{~V} / \mathrm{m}. The molecular polarizability is 2.33 \times 10^{-41} farad-m^{2} and the density of helium is 20.6 \times 10^{25} molecule \mathrm{m}^{3}.

Option: 1

4.76 \times 10^{-9} \mathrm{c} / \mathrm{m}^{2}


Option: 2

6.44 \times 10^{-9} \mathrm{c} / \mathrm{m}^{2}


Option: 3

5.64 \times 10^{-9} \mathrm{~c} / \mathrm{m}^{2}


Option: 4

2.88 \times 10^{-9} \mathrm{c} / \mathrm{m}^{2}


Answers (1)

best_answer

If p is the average dipole moment induced in each molecule then induced dipole moment per unit volume will be -

p=n p
Where n is the number of helium molecules per unit volume and p=\alpha \cdot E

Thus,
          \mathrm{P=n \: \propto\: E }
          \mathrm{P=20.6 \times 10^{25} \times 2.33 \times 10^{-41} \times 6 \times 10^{5} }
          \mathrm{P=2.88 \times 10^{-9} \mathrm{c} / \mathrm{m}^{2} }  Ans.

Posted by

Devendra Khairwa

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