Question

The natural abundance of \({ }^{3} \mathrm{He}\) is \(0.000137 \% .\) (a) How many protons, neutrons, and electrons are in an atom of \({ }^{3}\) He? (b) Based on the sum of the masses of their subatomic particles, which is expected to be more massive, an atom of \({ }^{3}\) He or an atom of \({ }^{3} \mathrm{H}\) (which is also called tritium)? (c) Based on your answer to part (b), what would need to be the precision of a mass spectrometer that is able to differentiate between peaks that are due to \({ }^{3} \mathrm{He}^{+}\) and \({ }^{3} \mathrm{H}^{+}\) ?

Short answer

A helium-3 atom has 2 protons, 1 neutron, and 2 electrons. The tritium atom is expected to be more massive than helium-3. The mass spectrometer should have a precision better than \(1.010\, u\) to differentiate between peaks due to helium-3 and tritium ions.

Step-by-step solution

(a) Determine the number of protons, neutrons, and electrons in a helium-3 atom

To determine the number of protons, neutrons, and electrons in a helium-3 atom, we need to analyze its atomic notation: \({ }^{3}\mathrm{He}\). The superscript 3 indicates the atomic mass number (A) which is the sum of protons and neutrons in the nucleus. The element symbol (He) represents helium, which has an atomic number (Z) of 2, indicating the number of protons in its nucleus. Number of protons (Z) = 2 Since the atom is electrically neutral, the number of electrons should also be equal to the number of protons. Number of electrons = 2 To find the number of neutrons, we need to subtract the number of protons from the atomic mass number (A). Number of neutrons (N) = A - Z = 3 - 2 = 1 So, a helium-3 atom has 2 protons, 1 neutron, and 2 electrons.

(b) Compare the sum of the masses of subatomic particles in helium-3 and tritium atoms

To compare the sum of the masses of subatomic particles in helium-3 and tritium atoms, we need to consider the masses of protons, neutrons, and electrons in each atom. For helium-3: Number of protons = 2, mass of 1 proton ≈ \(1.007\, u\) Number of neutrons = 1, mass of 1 neutron ≈ \(1.009\, u\) Number of electrons = 2, mass of 1 electron ≈ \(0.0005\, u\) Total mass of helium-3 atom ≈ 2\((1.007\, u)\) + \(1.009\, u\) + 2\((0.0005\, u)\) ≈ \(2.015\, u\) For tritium: Number of protons = 1, mass of 1 proton ≈ \(1.007\, u\) Number of neutrons = 2, mass of 1 neutron ≈ \(1.009\, u\) Number of electrons = 1, mass of 1 electron ≈ \(0.0005\, u\) Total mass of tritium atom ≈ \(1.007\, u\) + 2\((1.009\, u)\) + \(0.0005\, u\) ≈ \(3.025\, u\) Comparing the masses of helium-3 and tritium, we can conclude that tritium atom is expected to be more massive.

(c) Determine the precision of mass spectrometer

Based on the answer to part (b), we need to determine the precision of a mass spectrometer that can differentiate between helium-3 and tritium. To do this, we need to find the mass difference between the two ions of interest: Mass difference = Mass of \({ }^{3}\mathrm{T}^{+}\) - Mass of \({ }^{3}\mathrm{He}^{+}\) ≈ \(3.025\, u\) - \(2.015\, u\) ≈ \(1.010\, u\) The precision of the mass spectrometer needs to be smaller than the mass difference to differentiate between the two peaks: Precision of mass spectrometer < \(1.010\, u\) So, the mass spectrometer should have a precision better than \(1.010\, u\) to differentiate between peaks due to helium-3 and tritium ions.

Key concepts

Atomic Structure

Atomic structure is the fundamental concept that explains the composition of an atom. Every atom consists of a nucleus, housing protons and neutrons, surrounded by a cloud of electrons.

• The number of protons determines the atomic number, symbolized by \( Z \). This number is unique to each element. For helium, \( Z = 2 \), signifying two protons.
• Neutrons, along with protons, contribute to the atomic mass number \( A \), which is the sum of protons and neutrons. For helium-3, \( A = 3 \), leading to one neutron (\( A - Z = 3 - 2 \)).
• Electrons are equal in number to protons in a neutral atom. In helium-3, there are also two electrons.

Understanding atomic structure helps in grasping how atoms interact and form substances.

Mass Spectrometry

Mass spectrometry is a powerful analytical technique used to measure the mass of different particles. It helps identify and quantify substances by measuring the mass-to-charge ratio \((m/z)\) of ions.

• A sample is ionized, and the charged particles are guided through magnetic and electric fields.
• The deflection of ions depends on their mass and charge, allowing them to be detected and measured.
• Precision in mass spectrometry is crucial when differentiating between particles with small mass differences.

For instance, distinguishing between helium-3 \((^{3}He^{+})\) and tritium \((^{3}H^{+})\) requires a precision finer than \(1.010 \, u\), as their mass difference is approximately \(1.010 \, u\). This precision ensures accurate detection and differentiation of substances.

Helium-3

Helium-3 is a lighter isotope of helium. It is characterized by its unique atomic structure, having two protons, one neutron, and two electrons. Helium-3 is rare, with only 0.000137% natural abundance.

• This isotope plays a significant role in scientific research, particularly in cryogenics and nuclear fusion studies.
• It is stable, non-radioactive, and has applications in neutron detection technology.
• The unique energy states of helium-3 make it valuable for low-temperature physics experiments.

Understanding helium-3 involves recognizing its role both in natural and scientific contexts, emphasizing its importance beyond merely being an atom.