In radioactivity, the group displacement law describing how atomic number and mass number change during alpha and beta decay was proposed by which scientists?

Introduction / Context:
This question involves the group displacement law in radioactivity. The law explains how the position of an element in the periodic table changes when it undergoes alpha or beta decay. It was an important step in linking nuclear transformations to chemical periodicity and helped chemists correctly identify newly formed radioactive elements.

Given Data / Assumptions:

• The subject is the group displacement law in radioactive decay.
• We are asked which scientists proposed this law.
• Options include well known figures like Becquerel, Rutherford, Mendeleev, and the team of Frederick Soddy and Kasimir Fajans.
• We assume knowledge of basic radioactive processes: alpha decay and beta decay.

Concept / Approach:
The group displacement law states that when an atom emits an alpha particle, its atomic number decreases by 2 and its mass number decreases by 4, so it moves two places to the left in the periodic table. When an atom emits a beta particle (electron), its atomic number increases by 1 while its mass number remains unchanged, so it moves one place to the right in the periodic table. Frederick Soddy and Kasimir Fajans independently studied radioactive series and proposed this law, explaining how radioactive decay shifts elements between groups in the periodic table.

Step-by-Step Solution:
1) Identify that the group displacement law specifically connects nuclear decay (alpha and beta emission) with changes in atomic number and position in the periodic table.2) Recall that Henri Becquerel discovered radioactivity, but did not formulate the displacement law.3) Dmitri Mendeleev created the periodic table and predicted unknown elements, but his work predates the discovery of radioactivity.4) Ernest Rutherford investigated nuclear structure and alpha scattering but is not primarily associated with the group displacement law.5) Frederick Soddy and Kasimir Fajans independently analysed decay series and formulated the group displacement law summarising how alpha and beta emissions shift elements in the periodic table.6) Therefore, the law is correctly attributed to Soddy and Fajans.

Verification / Alternative check:
Textbooks on nuclear chemistry summarise the law as follows: emission of an alpha particle (helium nucleus) reduces atomic number by 2 and mass number by 4; emission of a beta particle increases atomic number by 1 without changing mass number. These predictable shifts in Z explain how elements in a radioactive series move across groups. The name Soddy Fajans displacement law appears in many references, confirming that these two scientists are credited with this formulation rather than Becquerel, Rutherford or Mendeleev.

Why Other Options Are Wrong:
Henri Becquerel: Discovered radioactivity in uranium salts but did not establish the group displacement law.
Ernest Rutherford: Known for the nuclear model of the atom and identification of alpha particles, not for the specific group law linking decay to periodic position.
Dmitri Mendeleev: Developed the periodic table, but his work came before the discovery of radioactivity.
James Chadwick and Niels Bohr: Chadwick discovered the neutron and Bohr formulated a model of the hydrogen atom; neither is associated with the group displacement law.

Common Pitfalls:
Students sometimes choose Rutherford or Becquerel because they strongly associate those names with radioactivity in general. However, the key is to link the specific term group displacement law with the names Soddy and Fajans. A useful memory tip is that Soddy worked extensively with radioactive series, and Fajans is known for both the displacement law and Fajans rules in bonding. Remembering these associations helps you avoid confusion when similar names appear together in nuclear chemistry questions.

Final Answer:
The group displacement law in radioactivity was proposed by Frederick Soddy and Kasimir Fajans.