Question

An \(\alpha\) particle is the nucleus of an \({ }^{4} \mathrm{He}\) atom. (a) How many protons and neutrons are in an \(\alpha\) particle? (b) What force holds the protons and neutrons together in the \(\alpha\) particle? (c) What is the charge on an \(\alpha\) particle in units of electronic charge? (d) The charge- to-mass ratio of an \(\alpha\) particle is \(4.8224 \times 10^{4} \mathrm{C} / \mathrm{g}\). Based on the charge on the particle, calculate its mass in grams and in amu. (e) By using the data in Table 2.1, compare your answer for part (d) with the sum of the masses of the individual subatomic particles. Can you explain the difference in mass? (If not, we will discuss such mass differences further in Chapter 21.)

Short answer

An alpha particle consists of 2 protons and 2 neutrons held together by the strong nuclear force. Its charge is +2 electronic charges. Its mass is approximately 6.643 x 10^-27 g or 3.999 amu. This differs from the sum of the individual subatomic particles' masses (4.032 amu) due to binding energy, which will be discussed in Chapter 21.

Step-by-step solution

Determine the number of protons and neutrons

Since an alpha particle is the nucleus of a helium atom with atomic number 2 and mass number 4 (denoted as \(^{4}\mathrm{He}\)), it means there are 2 protons and \(4 - 2 = 2\) neutrons.

Identify the force holding protons and neutrons together

The force that holds protons and neutrons together in the nucleus of an atom is called the strong nuclear force. This force operates over very short distances and is much stronger than the electrostatic forces between protons.

Calculate the charge on an alpha particle

An alpha particle contains 2 protons. Since each proton carries a positive charge of \(+1\) in units of electronic charge, the charge on an alpha particle is \(2 \times (+1) = +2\) electronic charges.

Calculate the mass of the alpha particle in grams and amu

We are given the charge-to-mass ratio, \(q/m = 4.8224 \times 10^{4} \mathrm{C/g}\). To find the mass, we need to rearrange the formula: \(m = \frac{q}{(4.8224 \times 10^{4} \mathrm{C/g})}\) For an alpha particle, the charge \(q\) is equal to the charge of two protons: \(q = 2 \times 1.602 \times 10^{-19}\mathrm{C}\). Thus, \(m = \frac{2 \times 1.602 \times 10^{-19}\mathrm{C}}{(4.8224 \times 10^{4}\mathrm{C/g})} \approx 6.643 \times 10^{-27}\mathrm{g}\) To convert the mass from grams to atomic mass units (amu), divide the mass in grams by the unified atomic mass unit \(u \approx 1.6605 \times 10^{-24}\mathrm{g}\): \(m_{\mathrm{amu}} =\frac{6.643 \times 10^{-27}\mathrm{g}}{1.6605 \times 10^{-24}\mathrm{g}} \approx 3.999\,\mathrm{amu}\)

Compare the alpha particle's mass with the sum of the masses of individual subatomic particles

The mass of a proton is approximately \(1.0073\,\mathrm{amu}\), and the mass of a neutron is approximately \(1.0087\,\mathrm{amu}\). The sum of the masses of two protons and two neutrons: \(2 \times (1.0073 \, \mathrm{amu}) + 2\times(1.0087\, \mathrm{amu}) = 4.032\,\mathrm{amu}\) Comparing the mass of the alpha particle with the sum of the individual subatomic particles, we find a difference: \(4.032\, \mathrm{amu} - 3.999\, \mathrm{amu} = 0.033\, \mathrm{amu}\) This difference is related to the binding energy of the nucleus, which is the energy needed to disassemble the nucleus into its individual protons and neutrons. To understand the mass difference better, nuclear reactions and the mass-energy equivalence given by Einstein's famous equation, \(E=mc^2\), will be discussed later in Chapter 21.

Key concepts

Protons and Neutrons in an Alpha Particle

An alpha particle is much more than just a high school chemistry concept; it's a window into the tiny, yet incredibly dense world within an atom's nucleus. Specifically, an alpha particle is identical to the nucleus of a helium-4 atom, composed of two protons and two neutrons. Why is this important? These particles are like the building blocks of the universe, forming heavier elements through fusion in stars.

Now, when it comes to helium, the lightest noble gas, the alpha particle gives it its chemical identity. Two protons determine helium's place as the second element on the periodic table, while the neutrons lend mass without altering its chemical properties. Together, these protons and neutrons provide a perfect natural example of nuclear stability in action.

Strong Nuclear Force

Imagine trying to push two powerfully magnetized positives ends together—they repel, right? This is the conundrum at the nucleus where protons, which are positively charged, are crammed incredibly close together. What stops them from blowing apart? The strong nuclear force. This fundamental force of nature is incredibly strong, as its name suggests, yet it operates over a minuscule range, effectively acting only within the nucleus.

The strength of this force is what allows the protons and neutrons in the small space of the alpha particle's nucleus to coexist without flying apart due to their like charges. It's the super glue of nuclear particles, binding them in a dance so tight that it takes immense energy to break them apart—a principle harnessed in nuclear reactors and weapons.

Charge-to-Mass Ratio of Particles

The charge-to-mass ratio is a critical concept that helps us characterize how particles like alpha particles behave in electric and magnetic fields. For alpha particles, this ratio is calculated by dividing the particle's total charge by its mass. For our tiny nuclear traveler, the alpha particle, this ratio provides insights into its mass without bouncing it off a scale.

This ratio greatly influences how particles travel through a magnetic or electric field. In other words, while an alpha particle might not carry around its weight information for all to see, by knowing its charge and how it zips through a field, scientists can back-calculate to determine the mass quite cleverly.

Atomic Mass Units and Mass Difference

When we talk about atomic mass units (amu), we're looking at a standardized scale to represent mass on an atomic or molecular level. Think of it as a minuscule unit of weight dedicated to the atomic realm, allowing chemists and physicists to communicate and calculate without lugging around unwieldy numbers.

But here's a kicker: the sum of the masses of protons and neutrons in an alpha particle doesn't quite measure up to the alpha particle's actual mass. This intriguing discrepancy, known as mass defect, hints at the binding energy that seals these particles together. Mass and energy are interchangeable, as Einstein's equation shows us, meaning that some of the mass is transformed into the energy needed to hold the nucleus together. It's a small but mighty example of how matter and energy are truly two sides of the same cosmic coin.