Question

Uranium- 235 undergoes a series of \(\alpha\) -particle and \(\beta\) -particle productions to end up as lead-207. How many \(\alpha\) particles and \(\beta\) particles are produced in the complete decay series?

Short answer

In the complete decay series of Uranium-235 to Lead-207, 5 α-particles and 15 β-particles are produced.

Step-by-step solution

Understand the decay processes of Uranium-235

We are given that Uranium-235 (U-235) decays through a series of α and β decays to become Lead-207 (Pb-207). The α-decay is the process in which an α-particle (which consists of 2 protons and 2 neutrons) is emitted from the nucleus of an atom. On the other hand, β-decay is the process in which a β-particle (an electron or positron) is emitted from the nucleus of an atom, changing a neutron into a proton. Keep in mind that in α-decay, the atomic number decreases by 2 and the mass number decreases by 4, whereas in β-decay, the atomic number increases by 1 and there is no change in the mass number.

Identify the chemical symbols and numbers of Uranium-235 and Lead-207

Before we can determine the number of α and β particles emitted during the decay series, we need to identify the chemical symbols and numbers of Uranium-235 and Lead-207. Uranium-235 can be represented as \(_{92}^{235}\textrm{U}\), where 92 is the atomic number (number of protons) and 235 is the mass number (number of protons + number of neutrons). Lead-207 can be represented as \(_{82}^{207}\textrm{Pb}\), where 82 is the atomic number and 207 is the mass number.

Calculate the change in atomic numbers and mass numbers

Now we find the difference in atomic numbers and mass numbers between Uranium-235 and Lead-207. Change in atomic number = Initial atomic number (U) - Final atomic number (Pb) = 92 - 82 = 10 Change in mass number = Initial mass number (U) - Final mass number (Pb) = 235 - 207 = 28

Determine the number of α-particles and β-particles emitted

We will use the changes in atomic numbers and mass numbers to find how many α-particles and β-particles are emitted in the decay series. Let x be the number of α-particles emitted and y be the number of β-particles emitted. We know that due to the emission of α-particles, the atomic number decreases by 2 and mass number decreases by 4. Therefore, we can write the following equation: 2x = 10 (change in atomic number) Solving for x, we get: x = 5 So, there are 5 α-particles emitted in the decay series. Next, we will determine the number of β-particles. In β-decay, the atomic number increases by 1 and there's no change in mass number. We already know the change in mass number is due to α-decay, so we don't need to consider it here. Using the change in atomic numbers, we can write the following equation: y - x = 10 But we already know the value of x (α-particles) is 5, so we can substitute it in the equation: y - 5 = 10 Solving for y, we get: y = 15 So, there are 15 β-particles emitted in the decay series.

Final answer

In the complete decay series of Uranium-235 to Lead-207, 5 α-particles and 15 β-particles are produced.

Key concepts

Uranium-235 Decay

The journey of Uranium-235 (₉₂U²³⁵) as it transforms into more stable elements is a complex process involving the emission of various particles. This natural radioactive decay series proceeds until the atom reaches a stable state, commonly ending as an isotope of lead. In the specific case of Uranium-235 decay, the atom undergoes a combination of alpha and beta particle emissions to finally become Lead-207 (₈₂Pb²⁰⁷). Understanding the nature of these emissions and their effects on the Uranium atom offers valuable insight into nuclear physics and helps us trace the steps in the atom's transformation.

Alpha Particle Emission

Alpha particle emission is a type of radioactive decay in which an atomic nucleus ejects an alpha particle. This particle consists of two protons and two neutrons, equivalently a helium-4 nucleus. When Uranium-235 emits an alpha particle, it loses exactly that: the mass number decreases by 4 (due to the loss of four nucleons), and the atomic number decreases by 2 (as it loses two protons), leading to the formation of a new element that is two places back in the periodic table.

Illustrating Alpha Decay:

Starting with Uranium-235, after releasing an alpha particle, the atom transforms into Thorium-231 (₉₀Th²³¹), as an example of alpha particle emission.

Beta Particle Emission

Conversely, beta particle emission occurs when a neutron in the nucleus of an atom is transformed into a proton and an electron. The emitted electron (or its antiparticle, the positron, in the case of positive beta decay), known as a beta particle, carries away the energy difference from this transformation. During this decay, the mass number remains unchanged since a neutron is replaced by a proton. However, the atomic number increases by 1, reflecting the additional proton and the atom's change into the next higher element on the periodic table.

Understanding Beta Decay:

After Thorium-231 undergoes beta decay, it becomes Protactinium-231 (₉₁Pa²³¹)—highlighting the gain in atomic number without a change in mass.

Atomic Number and Mass Number Changes

Keeping track of atomic number and mass number changes is vital when examining the decay series of radioactive elements like Uranium-235. The atomic number, which denotes the number of protons in an atom, dictates the element's identity, while the mass number represents the total number of protons and neutrons. During decay:

• An alpha particle emission reduces the atomic number by 2 and the mass number by 4.
• A beta particle emission increases the atomic number by 1 without affecting the mass number.

Using these principles, the transformation from Uranium-235 to Lead-207 entails a decrease of 10 in atomic number (from 92 to 82) and a decrease of 28 in mass number (from 235 to 207), as evidenced by a series of decays and the tally of emitted particles.