Question

Decay of which nucleus will lead to the following products: \((\mathbf{a})\) bismuth-211 by beta decay; \((\mathbf{b})\) chromium-so by positron emission; \((\mathbf{c})\) tantalum-179 by electron capture; \((\mathbf{d})\) radium-226 by alpha decay?

Short answer

The parent nuclei for each decay and their corresponding products are: a) Lead-211 (Pb-211) decays to Bismuth-211 (Bi-211) via beta decay. b) Manganese-50 (Mn-50) decays to Chromium-50 (Cr-50) via positron emission. c) Tungsten-179 (W-179) decays to Tantalum-179 (Ta-179) via electron capture. d) Thorium-230 (Th-230) decays to Radium-226 (Ra-226) via alpha decay.

Step-by-step solution

1. Beta decay

In beta decay, a neutron in the nucleus is converted into a proton, leading to the emission of an electron (beta particle). The mass number remains the same while the atomic number increases by 1. Given that the resulting nucleus is bismuth-211, let's find the parent nucleus. Let the parent nucleus be X. Since the atomic number of bismuth is 83, after beta decay, the atomic number of X must be 82. The mass number remains unchanged, so the mass number of X is also 211. Hence, the parent nucleus is lead-211 (Pb-211).

2. Positron emission

In positron emission, a proton is converted into a neutron, leading to the emission of a positron. The mass number remains the same while the atomic number decreases by 1. Given that the resulting nucleus is chromium-50, let's find the parent nucleus. Let the parent nucleus be Y. Since the atomic number of chromium is 24, before positron emission, the atomic number of Y must be 25. The mass number remains unchanged, so the mass number of Y is also 50. Hence, the parent nucleus is manganese-50 (Mn-50).

3. Electron capture

In electron capture, a proton in the nucleus captures a nearby electron and converts into a neutron. The mass number remains the same while the atomic number decreases by 1. Given that the resulting nucleus is tantalum-179, let's find the parent nucleus. Let the parent nucleus be Z. Since the atomic number of tantalum is 73, before electron capture, the atomic number of Z must be 74. The mass number remains unchanged, so the mass number of Z is also 179. Hence, the parent nucleus is tungsten-179 (W-179).

4. Alpha decay

In alpha decay, a nucleus emits an alpha particle, which consists of two protons and two neutrons. The mass number decreases by 4, while the atomic number decreases by 2. Given that the resulting nucleus is radium-226, let's find the parent nucleus. Let the parent nucleus be W. Since the atomic number of radium is 88, before alpha decay, the atomic number of W must be 90. The mass number decreases by 4, so the mass number of W is 230. Hence, the parent nucleus is thorium-230 (Th-230). In summary, the parent nuclei for each decay and their products are: a) Pb-211 ➝ Bi-211 (beta decay) b) Mn-50 ➝ Cr-50 (positron emission) c) W-179 ➝ Ta-179 (electron capture) d) Th-230 ➝ Ra-226 (alpha decay)

Key concepts

Beta Decay

Beta decay is a fascinating and common form of nuclear decay. It happens when a neutron in an atomic nucleus changes into a proton. This transformation releases an electron, which we call a beta particle.

Interestingly, during this process, the mass number of the atom remains unchanged, but the atomic number increases by one. This is because a neutron (which has no charge) becomes a proton (which has a positive charge). For example, in the beta decay of lead-211, the atomic number goes from 82 to 83, producing bismuth-211. However, the mass number stays at 211.

Beta decay is significant because it helps to stabilize a nucleus that has too many neutrons compared to protons. It plays a critical role in the nuclear reactions of stars and is crucial for the synthesis of new elements.

Alpha Decay

Alpha decay involves the emission of an alpha particle from the nucleus of an atom. An alpha particle is essentially a helium nucleus, consisting of two protons and two neutrons. When this happens, the atomic number of the original element decreases by two, and the mass number decreases by four.

For instance, the alpha decay of thorium-230 results in radium-226. This process decreases the atomic number by two, changing thorium with an atomic number of 90 to radium with an atomic number of 88. The mass number drops from 230 to 226.

Alpha decay is primarily observed in heavy elements like uranium and thorium and is a major means by which radioactive elements naturally lose mass. It's a spontaneous process and can be detected by the emission of helium nuclei from the decaying substance.

Electron Capture

Electron capture is a bit different from other nuclear decay processes. In this process, the nucleus absorbs one of the atom's own electrons from the innermost energy level. This electron combines with a proton to form a neutron.

As a result, the atomic number decreases by one, but the mass number remains the same, as a proton is merely converted into a neutron without losing or gaining nucleons. For instance, tungsten-179 transforms into tantalum-179 through electron capture. The atomic number reduces from 74 to 73, while the mass number remains 179.

This process is commonly observed in proton-rich isotopes where there are more protons compared to neutrons. Electron capture is crucial in the balance of protons and neutrons for elemental stability.

Positron Emission

In positron emission, a proton within the nucleus is converted into a neutron. This transformation ejects a positron, which is a particle like an electron but with a positive charge.

The atomic number of the element decreases by one due to the loss of a proton, while the mass number stays the same. In the case of manganese-50 undergoing positron emission, the atomic number decreases from 25 to 24, resulting in chromium-50, with an unchanged mass number of 50.

Positron emission is used in medical positron emission tomography (PET) scans, due to its ability to provide imaging in the body. It's an important decay process for understanding how certain isotopes lose protons to achieve a balanced nucleus.