Question

Decay of which nucleus will lead to the following products: (a) bismuth-211 by beta decay; (b) chromium-50 by positron emission; (c) tantalum-179 by electron capture; (d) radium-226 by alpha decay?

Short answer

The parent nuclei for each decay process are: (a) Lead-211 (Pb-211) decays to Bismuth-211 through Beta Decay, (b) Manganese-50 (Mn-50) decays to Chromium-50 through Positron Emission, (c) Tungsten-179 (W-179) decays to Tantalum-179 through Electron Capture, and (d) Thorium-230 (Th-230) decays to Radium-226 through Alpha Decay.

Step-by-step solution

(a) Bismuth-211 through Beta Decay

Beta decay is the process where a neutron in a nucleus is converted into a proton, which results in the emission of an electron, called a beta particle. Since bismuth-211 has 83 protons and 128 neutrons, to determine the parent nucleus, we just need to look for an element with 82 protons (because neutron changes into proton) and the same mass number, which is 211. The parent nucleus is lead-211 (Pb-211).

(b) Chromium-50 through Positron Emission

Positron emission is the process wherein a proton converts into a neutron, and a positron is emitted from the nucleus. For chromium-50, there are 24 protons and 26 neutrons. To find the parent nucleus, we need to look for an element with 25 protons (since proton changes into neutron) and a mass number of 50. The parent nucleus for this case is manganese-50 (Mn-50).

(c) Tantalum-179 through Electron Capture

In electron capture, a proton in the nucleus captures an electron from an inner electron shell, converting the proton into a neutron. For tantalum-179, there are 73 protons and 106 neutrons. To find the parent nucleus, we will look for an element with 74 protons (since proton captures the electron and converts to a neutron) and the same mass number, which is 179. The parent nucleus is tungsten-179 (W-179).

(d) Radium-226 through Alpha Decay

Alpha decay is characterized by the emission of an alpha particle, which consists of 2 protons and 2 neutrons, from the nucleus. Radium-226 has 88 protons and 138 neutrons. To find the parent nucleus, we need to look for an element with 90 protons (since 88 protons plus the 2 protons from the alpha particle) and a mass number of 230 (226 plus the 4 nucleons in the alpha particle). The parent nucleus is thorium-230 (Th-230).

Key concepts

Beta Decay

Beta decay is a fascinating process where a neutron in an atom's nucleus turns into a proton. During this transformation, the neutron ejects an electron, which is called a beta particle. This process occurs in elements that have an excess of neutrons. The overall mass number, which is the sum of protons and neutrons, stays the same, but the atomic number (the number of protons) increases by one.

• Neutron changes to a proton.
• Beta particle (electron) is emitted.
• Element's atomic number increases by 1.

For example, when bismuth-211 undergoes beta decay, it turns into lead-211. This is because one of its 128 neutrons transforms into a proton, changing the atomic number from 82 to 83 and releasing a beta particle.

Positron Emission

Positron emission is a type of nuclear decay where a proton inside the nucleus is converted into a neutron. This conversion causes the emission of a positron, which is the antimatter counterpart of an electron. It carries a positive charge. This process typically happens when there are too many protons in the nucleus compared to neutrons.

• Proton becomes a neutron.
• Positron (positively charged electron) is emitted.
• Element's atomic number decreases by 1.

Taking chromium-50 as an example, when it undergoes positron emission, it transforms into manganese-50. The atomic number decreases from 25 to 24, as a proton changes into a neutron, releasing a positron.

Electron Capture

Electron capture is a nuclear process where an inner-shell electron is captured by the nucleus. This electron combines with a proton to form a neutron. It's a unique way that unstable atoms can reduce their number of protons when there are too many.

• Inner electron combines with a proton.
• Forms a neutron.
• Element's atomic number decreases by 1.

For instance, tantalum-179 undergoes electron capture, turning into tungsten-179. One of its electrons is captured by the nucleus, and the atomic number decreases from 74 to 73.

Alpha Decay

Alpha decay is an interesting type of nuclear decay where the nucleus emits an alpha particle. An alpha particle is made up of two protons and two neutrons, essentially the same as a helium-4 nucleus. This kind of decay occurs in heavy elements where the nucleus is too large to be stable.

• Emission of an alpha particle (2 protons, 2 neutrons).
• Mass number decreases by 4.
• Atomic number decreases by 2.

In the case of radium-226, when it undergoes alpha decay, it becomes radon-222. The atomic number decreases from 88 to 86, and the mass number decreases from 226 to 222 as it emits an alpha particle.