Which fact indicates that the total energy of | vedclass

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(A) In an atom,the total energy $E$ of an electron is the sum of its kinetic energy $K$ and potential energy $U$. Since the electron is bound to the n

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The electron is attracted by the nucleus.

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(A) In an atom,the total energy $E$ of an electron is the sum of its kinetic energy $K$ and potential energy $U$. Since the electron is bound to the nucleus by the electrostatic force of attraction,the potential energy $U$ is negative. Mathematically,$U = -\frac{1}{4\pi\epsilon_0} \frac{Ze^2}{r}$. The kinetic energy $K$ is positive,given by $K = \frac{1}{2}mv^2 = \frac{1}{4\pi\epsilon_0} \frac{Ze^2}{2r}$. Thus,the total energy $E = K + U = -\frac{1}{4\pi\epsilon_0} \frac{Ze^2}{2r}$. $A$ negative total energy indicates that the electron is in a bound state,meaning it is attracted to the nucleus and requires external energy to be removed from the atom. Therefore,the fact that the electron is attracted by the nucleus is the reason for its negative total energy.

Which fact indicates that the total energy of an electron in an atom is negative?

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