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The numbers of protons, electrons and neutrons in a molecule of heavy water are respectively :
First, we need to understand what heavy water is. Heavy water is deuterium oxide, which is represented as $$ \text{D}_2\text{O} $$. This means one molecule of heavy water consists of two deuterium atoms and one oxygen atom.
Deuterium is an isotope of hydrogen. The atomic number of hydrogen is $$ 1 $$, which means it has $$ 1 $$ proton in its nucleus. Deuterium has a mass number of $$ 2 $$, so it has $$ 1 $$ proton and $$ 1 $$ neutron (since mass number = protons + neutrons, so neutrons = mass number - protons = $$ 2 - 1 = 1 $$). As a neutral atom, deuterium also has $$ 1 $$ electron.
Oxygen has an atomic number of $$ 8 $$, so it has $$ 8 $$ protons in its nucleus. The most common isotope of oxygen in heavy water is oxygen-16, with a mass number of $$ 16 $$. Therefore, it has $$ 16 - 8 = 8 $$ neutrons. As a neutral atom, oxygen has $$ 8 $$ electrons.
Now, for a molecule of heavy water, $$ \text{D}_2\text{O} $$, we calculate the total number of protons, electrons, and neutrons by adding the contributions from the two deuterium atoms and the one oxygen atom.
Total protons: Protons are in the nucleus and do not change when atoms form a molecule. Each deuterium atom has $$ 1 $$ proton, so two deuterium atoms contribute $$ 2 \times 1 = 2 $$ protons. The oxygen atom has $$ 8 $$ protons. Therefore, total protons = $$ 2 + 8 = 10 $$.
Total neutrons: Neutrons are also in the nucleus and do not change. Each deuterium atom has $$ 1 $$ neutron, so two deuterium atoms contribute $$ 2 \times 1 = 2 $$ neutrons. The oxygen atom has $$ 8 $$ neutrons. Therefore, total neutrons = $$ 2 + 8 = 10 $$.
Total electrons: In a neutral molecule, the total number of electrons equals the total number of protons, which is $$ 10 $$. We can also calculate it by adding the electrons from each atom. Each deuterium atom contributes $$ 1 $$ electron, so two deuterium atoms contribute $$ 2 \times 1 = 2 $$ electrons. The oxygen atom contributes $$ 8 $$ electrons. Therefore, total electrons = $$ 2 + 8 = 10 $$.
So, the numbers of protons, electrons, and neutrons in a molecule of heavy water are $$ 10 $$, $$ 10 $$, and $$ 10 $$ respectively.
Now, comparing with the options:
A. 8, 10, 11
B. 10, 10, 10
C. 10, 11, 10
D. 11, 10, 10
Option B matches our calculation.
Hence, the correct answer is Option B.
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