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The electric potential at the surface of an atomic nucleus (Z = 50) of radius of $ 9\times {{10}^{-5}}m $ is:
(A) 80 V
(B) $ 8\times {{10}^{6}}V $
(C) 9V
(D) $ 9\times {{10}^{5}}V $

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Last updated date: 18th Jun 2024
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Answer
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Hint
We should know that the electric potential, or voltage, is the difference in potential energy per unit charge between two locations in an electric field. When we talked about electric fields, we chose a location and then asked what the electric force would do to an imaginary positively charged particle if we put one there. Electric potential has the dimension length squared mass per electron current time cubed. The SI unit of electric potential is the volt, which is defined as a joule per coulomb. An atomic volt is defined as Hartree per electron, approximately volts. Voltage is changed in electric potential and when there is change in potential an electric field will be generated which causes the free electrons in the electric devices to move in a specific direction which is opposite to the direction of the electric field that is from negative to positive direction and thus current is produced. Based on this concept we have to solve this question.

Complete step by step answer
 We know that,
The total charge in the nucleus is $ \mathrm{q}=\mathrm{Ze} $ .
Therefore, the electric potential at the surface of the nucleus is $ \mathrm{V}=\dfrac{1}{4 \pi \epsilon_{0}} \dfrac{\mathrm{q}}{\mathrm{r}}=\dfrac{1}{4 \pi \epsilon_{0}} \dfrac{\mathrm{Ze}}{\mathrm{r}} $
or $ \mathrm{V}=\left(9 \times 10^{9}\right) \times \dfrac{50 \times 1.6 \times 10^{-19}}{9 \times 10^{-15}}=8 \times 10^{6} \mathrm{V} $
Therefore, the correct answer is Option (B).

Note
We should know that an atom consists of a positively charged nucleus, surrounded by one or more negatively charged particles called electrons. The positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. The nucleus has an overall positive charge as it contains the protons. Every atom has no overall charge neutral. This is because they contain equal numbers of positive protons and negative electrons. These opposite charges cancel each other out making the atom neutral. Since an atom has a finite number of protons and neutrons, it will generally emit particles until it gets to a point where its half-life is so long, it is effectively stable. It undergoes something known as alpha decay, and its half-life is over a billion times longer than the current estimated age of the universe.