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The mass of a $\mathrm{H}-$ atom is less than the sum of the masses of a proton and electron. Why is this?
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Verified Answer
We know that, The difference in mass of a nucleus and its constituents, $\Delta \mathrm{M}$, is called the mass defect and is
$$
\Delta \mathrm{M}=\left[\mathrm{Zm}_{\mathrm{p}}+(\mathrm{A}-\mathrm{Z}) \mathrm{m}_{\mathrm{n}}\right]-\mathrm{M}
$$
and the binding energy is $B=$ mass $\operatorname{defect}(\Delta M) \times c^2$.
So, the mass of a $\mathrm{H}$ - atom is
$\mathrm{m}_{\mathrm{p}}+\mathrm{m}_{\mathrm{e}}-\frac{\text { B.E }}{\mathrm{c}^2}$, where B.E $=13.6 \mathrm{eV}$ is the binding energy.
$$
\Delta \mathrm{M}=\left[\mathrm{Zm}_{\mathrm{p}}+(\mathrm{A}-\mathrm{Z}) \mathrm{m}_{\mathrm{n}}\right]-\mathrm{M}
$$
and the binding energy is $B=$ mass $\operatorname{defect}(\Delta M) \times c^2$.
So, the mass of a $\mathrm{H}$ - atom is
$\mathrm{m}_{\mathrm{p}}+\mathrm{m}_{\mathrm{e}}-\frac{\text { B.E }}{\mathrm{c}^2}$, where B.E $=13.6 \mathrm{eV}$ is the binding energy.
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