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Page 682: Lesson Check
$textbf{(b)}$ The $best$ explanation is
A. To give the object a positive charge means removing some of the electrons. This will reduce its mass.
$textbf{(b)}$ The charge of electron is $-e$ and the charge of proton is $+e$, so the total charge of the system is
$$
55(-e) + 43(e) = -12e = -12(1.6times10^{-19};mathrm{C}) = -1.9times10^{-18};mathrm{C}.
$$
$$
p(e) + 150(-e) = 22e ;;Rightarrow;; p – 150 = 22,
$$
where we used the fact that each electron has a charge of $-e$ charge and each proton has a charge of $+e$. Solving for $p$ gives us $p = 172$. Since the mass of proton is $m_p = 1.67times10^{-27}$ kg and the mass of electron is $m_e = 9.11times10^{-31}$ kg, the total mass of the system is
$$
begin{align*}
172m_p + 150m_e &= 172(1.67times10^{-27};mathrm{kg}) + 150(9.11times10^{-31};mathrm{kg})\
&= 2.87times10^{-25};mathrm{kg}.
end{align*}
$$
$$
n(-e) + 320(+e) = -51e ;;Rightarrow;; -n + 320 = -51,
$$
where we used the fact that each electron has a charge of $-e$ and each proton has a charge of $+e$. Solving for $n$ gives us $n = 371$. Since the mass of proton is $m_p = 1.67times10^{-27}$ kg and the mass of electron is $m_e = 9.11times10^{-31}$ kg, the total mass of the system is
$$
begin{align*}
320m_p + 371m_e &= 320(1.67times10^{-27};mathrm{kg}) + 371(9.11times10^{-31};mathrm{kg})\
&= 5.35times10^{-25};mathrm{kg}.
end{align*}
$$
$$
begin{align*}
3;mathrm{moles}&left(frac{6.022times10^{23};mathrm{atoms}}{mathrm{mole}}right)left(frac{18;mathrm{protons}}{mathrm{atom}}right)left(frac{1.60times10^{-19};mathrm{C}}{mathrm{proton}}right)\
&= 5.20times10^6;mathrm{C}.
end{align*}
$$
5.20times10^6;mathrm{C}
$$