Understanding the Relationship Between Alpha Decay, Half-Life, and Energy

The question asks about the scientists who discovered an important empirical relationship in nuclear physics concerning alpha decay. Specifically, it relates the half-life of a radioactive substance undergoing alpha decay to the energy of the alpha particles emitted.

Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (consisting of two protons and two neutrons, identical to a helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number decreased by four and an atomic number decreased by two.

The half-life of a radioactive substance is the time required for half of the atomic nuclei of a radioactive sample to decay.

The energy of the emitted alpha particle is kinetic energy. It is released during the decay process.

The Geiger-Nuttall Law

In 1911, Hans Geiger and Ernest Marsden (under Ernest Rutherford's supervision) conducted experiments scattering alpha particles. Later, in the same year, Hans Geiger and John Mitchell Nuttall established an empirical rule relating the decay constant (which is inversely proportional to the half-life) of an alpha-emitting isotope to the range of the alpha particles in air. Since the range of an alpha particle is directly related to its initial kinetic energy, this empirical relationship effectively connected the half-life of alpha decay to the energy of the emitted alpha particles.

The relationship found is known as the Geiger-Nuttall law. It can be expressed in different forms, but generally states that isotopes with shorter half-lives emit alpha particles with higher energies, and conversely, isotopes with longer half-lives emit alpha particles with lower energies. This is a semi-logarithmic relationship, often written as:

\(\log_{10} \lambda = A \log_{10} E + B\)

Where:

• \(\lambda\) is the decay constant (\(\lambda = \ln(2) / T_{1/2}\), where \(T_{1/2}\) is the half-life)
• \(E\) is the energy of the alpha particle
• \(A\) and \(B\) are constants

Alternatively, in terms of half-life (\(T_{1/2}\)):

\(\log_{10} T_{1/2} = -A \log_{10} E - B'\)

This means there is a strong inverse relationship between the logarithm of the half-life and the logarithm of the alpha particle energy.

Analyzing the Options

Let's look at the given options:

• Fermi and Meitner: Enrico Fermi is known for his work on beta decay theory and nuclear reactors. Lise Meitner was a key figure in the discovery of nuclear fission. While important in nuclear physics, they are not primarily associated with the empirical half-life and alpha energy relationship discovered in 1911.
• Geiger and Nuttall: Hans Geiger and John Mitchell Nuttall are credited with discovering the empirical relationship between the range (and thus energy) of alpha particles and the decay constant (and thus half-life) of alpha emitters in 1911. This aligns directly with the question.
• Chadwick and Lawrence: James Chadwick discovered the neutron. Ernest Lawrence invented the cyclotron. Their contributions are significant in nuclear physics but are not the empirical relationship in question.
• Soddy and Aston: Frederick Soddy worked on radioactivity and isotopes, receiving the Nobel Prize. Francis Aston developed the mass spectrograph and studied isotopes' masses. Their work is related to nuclear science but not this specific alpha decay relationship.

Based on the historical context and the relationship described (the Geiger-Nuttall law), the scientists who found the empirical relationship between the half-life of alpha decay and the energy of emitted alpha particles in 1911 were Geiger and Nuttall.

Conclusion on Alpha Decay Relationship

The empirical relationship described, linking alpha decay half-life and alpha particle energy, was indeed discovered by Geiger and Nuttall in 1911. This discovery was a significant step in understanding alpha decay and paved the way for later theoretical explanations like Gamow's quantum tunneling theory.

Revision Table: Key Concepts in Alpha Decay

Additional Information on Geiger-Nuttall Law

The Geiger-Nuttall law, while empirical, provided crucial data that theoretical physicists later sought to explain. George Gamow and, independently, Ronald Gurney and Edward Condon, explained this relationship in 1928 using quantum mechanics, specifically the concept of quantum tunneling. They showed that the probability of an alpha particle escaping the nucleus depends sensitively on its energy and the nuclear potential barrier, thus explaining the strong dependence of half-life on energy observed empirically by Geiger and Nuttall.

The extreme sensitivity of the half-life to energy is remarkable. A small change in alpha particle energy can lead to a change in half-life spanning many orders of magnitude. This was a key feature captured by the Geiger-Nuttall law and later explained by quantum tunneling.