Question

Write the symbols, including the atomic and mass numbers, for the radionuclides that would give each of the following products: (a) fermium- 257 by alpha emission, (b) bismuth- 211 by beta emission, (c) neodymium- 141 by positron emission, (d) tantalum-179 by electron capture.

Short answer

The parent radionuclides for the given products are: (a) nobelium-261 (_{102}^{261}No), (b) thallium-211 (_{82}^{211}Tl), (c) promethium-141 (_{61}^{141}Pm), (d) tungsten-179 (_{74}^{179}W).

Step-by-step solution

Understanding Alpha Emission

Alpha emission involves an atom losing an alpha particle, which consists of 2 protons and 2 neutrons, resulting in a decrease of atomic number by 2 and a mass number by 4. The parent nucleus will thus have an atomic number 2 units higher and a mass number 4 units higher than the daughter nucleus.

Identifying the Parent Nucleus for Fermium-257

Since fermium-257 (_{100}^{257}Fm) emits an alpha particle to become another element, we must find the element with an atomic number 2 units higher (102) and a mass number 4 units higher (261). This element is nobelium-261 (_{102}^{261}No).

Understanding Beta Emission

Beta emission involves an atom emitting a beta particle, which is an electron. This increases the atomic number by 1 as a neutron is converted into a proton, but leaves the mass number unchanged.

Identifying the Parent Nucleus for Bismuth-211

Since bismuth-211 (_{83}^{211}Bi) emits a beta particle, the parent nucleus must have an atomic number 1 unit lower (82) and the same mass number (211). This element is thallium-211 (_{82}^{211}Tl).

Understanding Positron Emission

Positron emission involves an atom emitting a positron, resulting in the decrease of the atomic number by 1 (as a proton is converted into a neutron) but keeps the mass number unchanged.

Identifying the Parent Nucleus for Neodymium-141

Since neodymium-141 (_{60}^{141}Nd) emits a positron, the parent nucleus must have an atomic number 1 unit higher (61) and the same mass number (141). This element is promethium-141 (_{61}^{141}Pm).

Understanding Electron Capture

Electron capture involves an atom absorbing an inner electron which combines with a proton to form a neutron, decreasing the atomic number by 1 without changing the mass number.

Identifying the Parent Nucleus for Tantalum-179

Since tantalum-179 (_{73}^{179}Ta) undergoes electron capture to become another element, the parent nucleus will have an atomic number 1 unit higher (74) and the same mass number (179). This element is tungsten-179 (_{74}^{179}W).

Key concepts

Alpha Emission

Alpha emission is a type of radioactive decay where an unstable atom ejects an alpha particle, composed of two protons and two neutrons. Imagine it as a tiny helium nucleus being shot out of the atom. This process results in the transformation of the original atom into a new element with an atomic number reduced by 2 and a mass number decreased by 4.

For instance, when fermium-257 undergoes alpha emission, it releases an alpha particle to become nobelium-261. In general terms, if an element \( _{Z}^{A}X \) emits an alpha particle, the new element formed would be \( _{Z-2}^{A-4}Y \).

Key Takeaways of Alpha Emission:

• An alpha particle is similar to a helium nucleus.
• Alpha emission decreases the atom's atomic number by 2 and the mass number by 4.
• The process results in a new, lighter element.

Beta Emission

Beta emission represents another avenue of radioactive decay. In beta emission, a neutron within an atom's nucleus is transformed into a proton, and an electron (called a beta particle) is ejected. Surprisingly, despite a particle being ejected, the mass number stays unchanged, but the atomic number increases by 1.

When looking at bismuth-211, which becomes a different element after emitting a beta particle, we deduce that its predecessor is thallium-211. The parent atom \( _{Z}^{A}X \) transforms to \( _{Z+1}^{A}Y \) post-beta emission.

Key Understandings of Beta Emission:

• The ejected beta particle is an electron.
• Transforms a neutron into a proton, increasing atomic number by 1.
• The mass number remains constant despite the decay process.

Positron Emission

Positron emission is a bit like beta emission's mirror image. Instead of emitting an electron, the atom emits a positron, which is the antimatter counterpart of an electron. Through this process, a proton in the nucleus is transformed into a neutron, causing a decrease in the atomic number by 1. However, just like beta emission, the mass number remains the same.

Taking neodymium-141 as an example, which emits a positron to transform, we can trace it back to its parent, promethium-141. Generally, if an atom \( _{Z}^{A}X \) goes through positron emission, it becomes \( _{Z-1}^{A}Y \).

Important Aspects of Positron Emission:

• A positron is the antiparticle of an electron.
• Positron emission decreases the atomic number by 1 while mass number stays unchanged.
• Results in a conversion of a proton to a neutron within the nucleus.

Electron Capture

Electron capture is a lesser-known form of radioactive decay, but it's fascinating. Rather than emitting a particle, the atom's nucleus actually captures one of its own electrons. This usually occurs with one of the innermost electrons. When captured, the electron combines with a proton to form a neutron, subsequently reducing the atomic number by 1 without altering the mass number.

In the case of tantalum-179, we can infer that it was once tungsten-179 before capturing an electron. Formally, if an element \( _{Z}^{A}X \) captures an electron, it transforms into \( _{Z-1}^{A}Y \).

Crucial Points on Electron Capture:

• Electron capture is an inward process where an electron is absorbed by the nucleus.
• Decreases an atom's atomic number by 1, while the mass number remains the same.
• It converts a proton to a neutron and forms a new element.