To determine the number of neutrons in a 3-gram sample of hydrogen gas containing hydrogen and deuterium atoms in an atomic ratio of 6000:1, we need to calculate the approximate mass contribution of each isotope and then convert it to the number of neutrons.
The atomic mass of hydrogen (H) is approximately 1.008 amu, and the atomic mass of deuterium (D) is approximately 2.014 amu.
Given that the atomic ratio of hydrogen to deuterium is 6000:1, we can calculate the mass contribution of each isotope in the 3-gram sample.
Mass of hydrogen (H) in the sample: Mass of H = (6000/6001) * 3 g ≈ 2.997 g
Mass of deuterium (D) in the sample: Mass of D = (1/6001) * 3 g ≈ 0.0005 g
Now we can convert the mass of each isotope to the number of moles using their respective molar masses.
Molar mass of hydrogen (H) = 1.008 g/mol Molar mass of deuterium (D) = 2.014 g/mol
Number of moles of hydrogen (H): Moles of H = (Mass of H) / (Molar mass of H) ≈ 2.997 g / 1.008 g/mol ≈ 2.972 mol
Number of moles of deuterium (D): Moles of D = (Mass of D) / (Molar mass of D) ≈ 0.0005 g / 2.014 g/mol ≈ 0.000249 mol
Since both hydrogen and deuterium have one neutron each, the number of neutrons in the sample is approximately equal to the total number of moles of hydrogen and deuterium.
Number of neutrons = Moles of H + Moles of D ≈ 2.972 mol + 0.000249 mol ≈ 2.972249 mol
To convert this value to the number of neutrons, we need to multiply by Avogadro's number, which is approximately 6.022 × 10^23 neutrons/mol.
Number of neutrons ≈ 2.972249 mol * 6.022 × 10^23 neutrons/mol ≈ 1.79 × 10^24 neutrons
Therefore, the number of neutrons in a 3-gram sample of hydrogen gas containing hydrogen and deuterium atoms in the atomic ratio 6000:1 is approximately 1.79 × 10^24 neutrons.