The total energy of an electron in the first excited state of the hydrogen atom is about $-3.4 \; eV.$
$(a)$ What is the kinetic energy of the electron in this state?
$(b)$ What is the potential energy of the electron in this state?
$(c)$ Which of the answers above would change if the choice of the zero of potential energy is changed?
$(a)$ What is the kinetic energy of the electron in this state?
$(b)$ What is the potential energy of the electron in this state?
$(c)$ Which of the answers above would change if the choice of the zero of potential energy is changed?
(N/A) The total energy of the electron is $E = -3.4 \; eV$. The kinetic energy $(K)$ of an electron in a hydrogen atom is equal to the negative of its total energy.
$\Rightarrow K = -E$
$K = -(-3.4 \; eV) = +3.4 \; eV$
Thus,the kinetic energy of the electron in this state is $+3.4 \; eV$.
$(b)$ The potential energy $(U)$ of the electron in a hydrogen atom is equal to $-2$ times its kinetic energy.
$\Rightarrow U = -2K$
$U = -2 \times 3.4 \; eV = -6.8 \; eV$
Thus,the potential energy of the electron in this state is $-6.8 \; eV$.
$(c)$ Potential energy is defined relative to a reference point where it is assumed to be zero. If the reference point is changed,the potential energy $(U)$ and consequently the total energy $(E = K + U)$ will change. However,the kinetic energy $(K)$ remains unchanged because it depends only on the velocity of the electron.
$\Rightarrow K = -E$
$K = -(-3.4 \; eV) = +3.4 \; eV$
Thus,the kinetic energy of the electron in this state is $+3.4 \; eV$.
$(b)$ The potential energy $(U)$ of the electron in a hydrogen atom is equal to $-2$ times its kinetic energy.
$\Rightarrow U = -2K$
$U = -2 \times 3.4 \; eV = -6.8 \; eV$
Thus,the potential energy of the electron in this state is $-6.8 \; eV$.
$(c)$ Potential energy is defined relative to a reference point where it is assumed to be zero. If the reference point is changed,the potential energy $(U)$ and consequently the total energy $(E = K + U)$ will change. However,the kinetic energy $(K)$ remains unchanged because it depends only on the velocity of the electron.
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