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Law Of Radioactivity Decay

Law Of Radioactivity Decay

Edited By Vishal kumar | Updated on Jul 02, 2025 08:01 PM IST

The Law of Radioactive Decay elucidates the method through which unstable atomic nuclei lose energy. This occurs because the unstable core transmutes itself into another core element when it decays releasing some particles or electromagnetic waves in the process. For given radioactive compounds, the time-lapse for this change is always constant meaning that it occurs at a specific speed so that half of any given amount gets exhausted after some time.

This Story also Contains
  1. Radioactivity
  2. What is Half-life (T1/2)?
  3. Mean or Average life $\left(T_{\text {mean }}\right)$
  4. Solved Examples Based on the Law of Radioactivity Decay
  5. Summary
Law Of Radioactivity Decay
Law Of Radioactivity Decay

The radioactive decay law is one of the cornerstones of nuclear physics that solves the problem of unstable atomic nuclei losing energy as they emit some radiation continuously. Meanwhile, this entire process usually conforms to exponential decay which implies that the radioactive material goes down by proportionate amounts each time. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of thirty questions have been asked on this concept. For NEET eight questions were asked from this concept.

Radioactivity

The phenomenon by virtue of which a substance, spontaneously, disintegrates by emitting certain radiations is called radioactivity.

Activity (A)

Activity is measured in terms of disintegration per second.

$A=-\frac{d N}{d t}$

Units of Radioactivity

Its SI unit is 'Bq (Becquerel)'.

Curie ( Ci ):- Radioactivity of a substance is said to be one curie if its atoms disintegrate at the rate of $3.7 \times 10^{10}$ disintegrations per second. I.e $1 \mathrm{Ci}=3.7 \times 10^{10} \mathrm{~Bq}=37 \mathrm{GBq}$

Rutherford (Rd):- Radioactivity of a substance is said to be 1 Rutherford if its atoms disintegrate at the rate of 106 disintegrations per second.

The relation between Curie and Rutherford- 1 C = 3.7×104 Rd

Laws of Radioactivity

Radioactivity is due to the disintegration of a nucleus. The disintegration is accompanied by the emission of energy in terms of α, β and γ-rays either single or all at a time. The rate of disintegration is not affected by external conditions like temperature and pressure etc.

According to Laws of radioactivity the rate of the disintegration of the radioactive substance, at any instant, is directly proportional to the number of atoms present at that instant.
$
\text { i.e }-\frac{d N}{d t}=\lambda N
$

where $\lambda=$ disintegration constant or radioactive decay constant
- Number of nuclei after the disintegration (N)

$
N=N_0 e^{-\lambda t}
$

where $\mathrm{N}_0$ is the number of radioactive nuclei in the sample at $\mathrm{t}=0$.
Similarly, the Activity of a radioactive sample at time $t$

$
A=A_0 e^{-\lambda t}
$

where A0 is the Activity of a radioactive sample at time t =0

What is Half-life (T1/2)?

The half-life of a radioactive substance is defined as the time during which the number of atoms of the substance is reduced to half their original value.

$\mathrm{T}_{1 / 2}=\frac{0.693}{\lambda}$

Thus, the half-life of a radioactive substance is inversely proportional to its radioactive decay constant.

Number of nuclei in terms of half-life

$N=\frac{N_0}{2^{t / T_{1 / 2}}}$

Note- It is a very useful formula to determine the number of nuclei after the disintegration in terms of half-life

Mean or Average life $\left(T_{\text {mean }}\right)$

Definition: The arithmetic mean of the lives of all the atoms is known as the mean life or average life of the radioactive substance.

Tmean = sum of lives of all atoms / total number of atoms

Let |dN| be the number of nuclei decaying between t, t + dt; the modulus sign is required to ensure that it is positive.

$\begin{aligned} & \mathrm{dN}=-\lambda \mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}} \mathrm{dt} \\ & \text { and }|\mathrm{d} N|=\lambda \mathrm{N}_0 \mathrm{e}^{-\lambda t} \mathrm{dt} \\ & T_{\text {mean }}=\frac{\int_0^{\infty} t|d N|}{\int_0^{\infty}|d N|}=\frac{\frac{1}{\lambda^2}}{\frac{1}{\lambda}}=\frac{1}{\lambda} \\ & \Rightarrow T_{\text {mean }}=\frac{1}{\lambda}\end{aligned}$

The average life of a radioactive substance is equal to the reciprocal of its radioactive decay constant.

The average life of a radioactive substance is also defined as the time in which the number of nuclei reduces to $\left(\frac{1}{e}\right)$ part of the initial number of nuclei.

The Relation Between $T_{1 / 2}$ and $T_{\text {mean }}$

$
\rightarrow T_{1 / 2}=(0.693) T_{\text {mean }}
$
OR

$
\text { Half-life }=(0.693) \text { Mean life }
$

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Solved Examples Based on the Law of Radioactivity Decay

Example 1: A radioactive element $X$ with half life 2 h decays giving a stable element Y . After a time $t$, the ratio of X and Y atoms is $1: 16$. Time $t$ is:

1) 6 h

2) 4 h

3) 8 h

4) 16 h

Solution:

$\begin{aligned} & \frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^{\mathrm{n}}=\frac{1}{16} \\ & \because \quad \mathrm{n}=4 \\ & \therefore \quad \mathrm{t}=\mathrm{nT}_{1 / 2}=4 \times 2=8 \mathrm{~h}\end{aligned}$

Hence, the answer is the option (3).

Example 2: Two radioactive substances $A$ and $B$ have decay constant $5 \lambda$ and $\lambda$ respectively. At $t=0$, they have the same number of nuclei. The ratio of a number of nuclei of $A$ to that of $B$ will be $(1 / e)^2$ after a time interval of:

1) $\frac{1}{\lambda}$
2) $\frac{1}{2 \lambda}$
3) $\frac{1}{3 \lambda}$
4) $\frac{1}{4 \lambda}$

Solution:

According to radioactive decay, $\mathrm{N}=\mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}}$
Where, $\mathrm{N}_0=$ Number of radioactive nuclei present in the sample at $\mathrm{t}=0$
$\mathrm{N}=$ Number of radioactive nuclei left undecayed after time t
$\lambda=$ decay constant
For $\mathrm{A}, \mathrm{N}_{\mathrm{A}}=\left(\mathrm{N}_0\right) \mathrm{Ae}^{-5 \lambda t}$
For $B, N_B=\left(N_0\right) \mathrm{Be}^{-\lambda t}$
As per question $\left(\mathrm{N}_0\right)_{\mathrm{A}}=\left(\mathrm{N}_0\right)_{\mathrm{B}}$ (Given)
Dividing (i) by (ii), we get

$
\begin{aligned}
& \frac{N_A}{N_B}=\frac{e^{-5 \lambda t}}{e^{-\lambda t}}=e^{-4 \lambda t} \quad \text { or }\left(\frac{1}{e}\right)^2=e^{-4 \lambda t} \quad \text { or } \quad \frac{1}{e^2}=\frac{1}{e^{4 \lambda t}} \\
& e^{4 \lambda t}=e^2 \quad \text { or } \quad 4 \lambda t=2 \quad \text { or } \quad t=\frac{2}{4 \lambda}=\frac{1}{2 \lambda}
\end{aligned}
$

Hence, the answer is the option (2).

Example 3: The half-life of the radioactive nucleus is 50 days. The time interval $\left(t_2-t_1\right)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and the time $t_1$ when $\frac{1}{3}$ of it had decayed is:

1) 30 days

2) 50 days

3) 60 days

4) 15 days

Solution:

According to radioactive decay law $\mathrm{N}=\mathrm{N}_0 \mathrm{e}^{-\lambda t}$
Where the Number of radioactive nuclei at the time $t=0$
$\mathrm{N}=$ Number of radioactive nuclei left undecayed at any time t
$\lambda=$ decay constant
At the time $t_2, \frac{2}{3}$ of the sample had decayed

$
\therefore \mathrm{N}=\frac{1}{3} \mathrm{~N}_0 \quad \text { or } \quad \frac{1}{3} \mathrm{~N}_0=\mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}_2}
$
At the time $t_1, \frac{1}{3}$ of the sample had decayed,

$
\therefore \mathrm{N}=\frac{2}{3} \mathrm{~N}_0 \quad \text { or } \quad \frac{2}{3} \mathrm{~N}_0=\mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}_1}
$
Divide (i) by (ii), we get
$\frac{1}{2}=\frac{e^{-\lambda t_2}}{e^{-\lambda t_1}} \quad$ or $\quad \frac{1}{2}=e^{-\lambda\left(t_2-t_1\right)} \quad$ or $\quad \lambda\left(t_2-t_1\right)=\ln 2$
$\mathrm{t}_2-\mathrm{t}_1=\frac{\ln 2}{\lambda}=\frac{\ln 2}{\left(\frac{\ln 2}{\mathrm{~T}_{1 / 2}}\right)} \quad\left(\because \lambda=\frac{\ln 2}{\mathrm{~T}_{1 / 2}}\right)$
$\mathrm{T}_{1 / 2}=50$ days

Hence, the answer is the option (2).

Example 4: A radioactive substance decays at the rate of 5000 disintegrations per minute. After 5 minutes it disintegrates at 1250 disintegration per minute. The decay constant is:

1) $0.2 \ln 2 \mathrm{~min}^{-1}$
2) $0.4 \ln 2 \mathrm{~min}^{-1}$
3) $0.6 \ln 2 \mathrm{~min}^{-1}$
4) $0.81 \ln 2 \mathrm{~min}^{-1}$

Solution:

The rate of disintegration R is given by $R=R_0 e^{-\lambda t}$
Where $R_0$ is the initial rate at $t=0$

$
\therefore \frac{\mathrm{R}_0}{\mathrm{R}}=\mathrm{e}^{\lambda \mathrm{t}}
$
Taking the natural logarithm on both sides, we get

$
\ln \left(\frac{\mathrm{R}_0}{\mathrm{R}}\right)=\lambda \mathrm{t} \quad \text { or } \quad \lambda=\frac{1}{\mathrm{t}} \ln \left(\frac{\mathrm{R}_0}{\mathrm{R}}\right)
$
According to the problem, $R_0=5000, R=1250, t=5 \mathrm{~min}$

$
\therefore \quad \lambda=\frac{1}{5} \ln \left(\frac{5000}{2000}\right)=\frac{1}{5} \ln 4=\frac{2}{5} \ln 2=0.4 \ln 2 \mathrm{~min}^{-1}
$

Hence, the answer is the option (2).

Example 5: The radioactivity of a sample is $X$ at a time $t_1$ and $Y$ at a time $t_2$. If the mean lifetime of the specimen is $\tau$, the number of atoms that have disintegrated in the time interval $\left(t_1-t_2\right)$ is:

1) $\mathrm{Xt}_1-\mathrm{Yt}_2$
2) $\mathrm{X}-\mathrm{Y}$
3) $\frac{X-Y}{\tau}$
4) $(X-Y) \tau$

Solution:

Activity at time $t_1$,

$
\mathrm{X}=\lambda \mathrm{N}_1=\frac{1}{\tau} \mathrm{N}_1 \quad \text { or } \quad \mathrm{N}_1=\tau \mathrm{X} \quad\left(\because \tau=\frac{1}{\lambda}\right)
$
Activity at time

$
\mathrm{t}_2, \mathrm{Y}=\lambda \mathrm{N}_2=\frac{1}{\tau} \mathrm{N}_2
$

or $\quad \mathrm{N}_2=\tau \mathrm{Y}$
Therefore, the number of nuclei decayed during time interval $\left(t_1-t_2\right)$ is

$
\mathrm{N}_1-\mathrm{N}_2=\tau \mathrm{X}-\tau \mathrm{Y}=(\mathrm{X}-\mathrm{Y}) \tau
$

Hence, the answer is the option (4).

Summary

Unstable atomic nuclei lose energy due to radioactivity. Different elements are formed after radiation causes nuclei to decay. This decay is disorganised but follows a routine pattern based on the half-life, i.e. the time taken for half of all radioactive atoms in the sample to disappear completely. In addition, the rate at which these radioactive atoms disappear completely is non-linear, it declines proportional to the remaining number of non-decayed nuclei in them.

Frequently Asked Questions (FAQs)

1. How is the rate of radioactive decay measured?
The rate of radioactive decay is measured using the decay constant (λ), which represents the probability of a single atom decaying in a unit of time. It's related to the half-life and is used in the exponential decay equation.
2. What is the relationship between half-life and decay constant?
The half-life (T₁/₂) and decay constant (λ) are inversely related. The mathematical relationship is: T₁/₂ = ln(2) / λ. This means that isotopes with shorter half-lives have larger decay constants, and vice versa.
3. What is meant by the term "activity" in radioactive decay?
Activity refers to the rate at which radioactive decays occur in a sample. It's measured in becquerels (Bq), where 1 Bq equals one decay per second. Activity decreases over time as the number of radioactive nuclei decreases.
4. How does the mass of a radioactive sample change over time?
The mass of a radioactive sample decreases very slightly over time as atoms decay. This is due to the conversion of a small amount of mass into energy (according to E=mc²) during the decay process. However, this mass change is usually negligible in practical measurements.
5. What is the significance of the decay chain in radioactive decay?
A decay chain is the series of radioactive decays that occur as an unstable parent isotope decays through various daughter products until a stable isotope is reached. Understanding decay chains is crucial for predicting the behavior and products of long-lived radioactive materials.
6. What is radioactive decay?
Radioactive decay is the spontaneous process by which an unstable atomic nucleus emits particles or energy to become more stable. This process occurs naturally and cannot be influenced by external factors like temperature or pressure.
7. Why do some atoms undergo radioactive decay while others don't?
Atoms undergo radioactive decay when their nuclei are unstable, typically due to an imbalance in the number of protons and neutrons. Stable atoms have a balanced ratio of protons to neutrons, while unstable atoms have an excess of either, leading to decay.
8. What is the exponential decay law?
The exponential decay law states that the number of radioactive nuclei in a sample decreases exponentially with time. It's expressed mathematically as N(t) = N₀e^(-λt), where N(t) is the number of nuclei at time t, N₀ is the initial number, and λ is the decay constant.
9. Can the rate of radioactive decay be changed by external factors?
No, the rate of radioactive decay is a fundamental property of the isotope and cannot be altered by external factors such as temperature, pressure, or chemical reactions. This constancy is what makes radioactive dating methods reliable.
10. Why is radioactive decay considered a statistical process?
Radioactive decay is considered statistical because it's impossible to predict exactly when a single atom will decay. We can only describe the probability of decay over time for a large number of atoms, which follows the exponential decay law.
11. How does the concept of nuclear matrix elements influence decay rates in beta and double-beta decay?
Nuclear matrix elements describe the transition probability between initial and final nuclear states in decay processes. They are crucial for calculating decay rates, especially in beta and double-beta decay. Accurate determination of these elements is challenging but essential for understanding decay processes and neutrino physics.
12. What is the half-life of a radioactive substance?
The half-life is the time it takes for half of the original amount of a radioactive substance to decay. It's a characteristic property of each radioactive isotope and can range from fractions of a second to billions of years.
13. How does the concept of half-life relate to carbon dating?
Carbon dating uses the half-life of carbon-14 (about 5,730 years) to estimate the age of organic materials. By measuring the ratio of carbon-14 to stable carbon-12 in a sample and comparing it to the known half-life, scientists can calculate how long ago the organism died.
14. How does the concept of radioactive equilibrium apply to decay chains?
Radioactive equilibrium occurs in a decay chain when the rate of production of a daughter nuclide equals its rate of decay. This happens when the half-life of the parent is much longer than that of the daughter. In this state, the ratio of parent to daughter atoms remains constant over time.
15. What is the importance of decay constants in radioactive dating techniques?
Decay constants are crucial in radioactive dating because they allow scientists to calculate the age of a sample based on the ratio of parent to daughter isotopes. The precision of these techniques depends on accurately knowing the decay constants of the relevant isotopes.
16. How does the concept of mean lifetime differ from half-life?
Mean lifetime (τ) is the average time that a radioactive atom exists before decaying. It's related to the half-life (T₁/₂) by the equation τ = T₁/₂ / ln(2). Mean lifetime is useful in certain calculations, but half-life is more commonly used due to its intuitive nature.
17. How does the shell model of the nucleus explain "magic numbers" in nuclear stability?
The shell model suggests that nucleons (protons and neutrons) occupy energy levels or "shells" within the nucleus. Nuclei with completely filled shells (corresponding to magic numbers of protons or neutrons) are particularly stable and less likely to undergo radioactive decay.
18. How does the concept of nuclear binding energy explain why very heavy nuclei tend to undergo fission?
Very heavy nuclei have lower binding energy per nucleon compared to medium-mass nuclei. This makes them less stable and prone to splitting into smaller nuclei (fission), which have higher binding energy per nucleon. This process releases energy and is the basis for nuclear power and weapons.
19. How does the concept of nuclear spin influence allowed and forbidden transitions in beta decay?
Nuclear spin determines the angular momentum of a nucleus. In beta decay, transitions between states must conserve angular momentum. This leads to selection rules that classify transitions as allowed or forbidden, affecting decay rates and energy spectra of emitted particles.
20. How does the concept of nuclear shell structure explain "islands of inversion" in exotic nuclei?
Islands of inversion are regions in the nuclear chart where the expected shell structure breaks down, leading to unexpected stability or instability. This phenomenon, observed in some exotic nuclei, challenges traditional models of nuclear structure and decay.
21. What is the significance of Fermi's theory of beta decay in understanding weak interactions?
Fermi's theory of beta decay was the first successful quantum mechanical description of weak interactions. It introduced the concept of neutrinos and laid the groundwork for understanding beta decay processes, including energy spectra and selection rules.
22. How does the concept of nuclear polarization affect electron capture decay rates?
Nuclear polarization refers to the distortion of the nuclear charge distribution due to the presence of atomic electrons. In electron capture decay, this effect can modify the overlap between electron and nuclear wavefunctions, influencing the decay rate. It's particularly important for precise calculations in astrophysical contexts.
23. What is the difference between radioactive decay and nuclear fission?
Radioactive decay is a spontaneous process where an unstable nucleus emits particles or energy to become more stable. Nuclear fission, on the other hand, is the splitting of a heavy nucleus into lighter nuclei, often induced by neutron bombardment and releasing significant energy.
24. How does radioactive decay relate to the concept of binding energy?
Radioactive decay occurs when nuclei have an excess of energy compared to their most stable configuration. This excess energy is related to the binding energy, which is the energy required to break a nucleus apart. Nuclei undergo decay to reach a state of higher binding energy per nucleon.
25. What is the difference between alpha, beta, and gamma decay?
Alpha decay involves the emission of a helium nucleus (2 protons and 2 neutrons), beta decay involves the emission of an electron or positron, and gamma decay involves the emission of high-energy photons. Each type changes the nucleus differently and has distinct penetrating abilities.
26. How does the atomic number change during different types of radioactive decay?
In alpha decay, the atomic number decreases by 2. In beta-minus decay, it increases by 1. In beta-plus decay, it decreases by 1. Gamma decay does not change the atomic number. These changes are crucial for understanding how elements transform during decay.
27. What is meant by the term "parent nuclide" and "daughter nuclide" in radioactive decay?
The parent nuclide is the original unstable isotope that undergoes radioactive decay. The daughter nuclide is the isotope produced after the decay process. In a decay chain, a daughter nuclide may itself be unstable and become a parent nuclide for the next decay.
28. What is the significance of branching decay?
Branching decay occurs when a radioactive isotope can decay in more than one way. For example, an isotope might undergo both alpha and beta decay with different probabilities. This complicates decay calculations but provides valuable information about nuclear structure and stability.
29. How does the neutron-to-proton ratio affect nuclear stability and decay modes?
Nuclei with too many neutrons relative to protons tend to undergo beta-minus decay, converting a neutron to a proton. Conversely, nuclei with too many protons relative to neutrons tend to undergo beta-plus decay or electron capture. This tendency drives nuclei towards the "valley of stability."
30. What is the significance of the N-Z curve in understanding nuclear stability?
The N-Z curve (neutron number vs. atomic number) helps visualize nuclear stability. Stable nuclei fall along a specific region of this curve called the "belt of stability." Nuclei far from this belt are unstable and undergo radioactive decay to move closer to the stable region.
31. What is the physical meaning of the decay constant?
The decay constant (λ) represents the probability per unit time that a single radioactive nucleus will decay. It's a fundamental property of each radioactive isotope and is independent of the sample size or the time since the sample was formed.
32. How does the concept of binding energy per nucleon relate to radioactive decay?
Binding energy per nucleon is a measure of nuclear stability. Nuclei with lower binding energy per nucleon are more likely to undergo radioactive decay. The decay process generally results in daughter nuclei with higher binding energy per nucleon, moving towards greater stability.
33. What is the significance of the "island of stability" in superheavy elements?
The "island of stability" is a hypothetical region of superheavy elements with relatively long half-lives, despite their high atomic numbers. This concept challenges the general trend of decreasing stability with increasing atomic number and is an active area of nuclear physics research.
34. How does quantum tunneling contribute to alpha decay?
Alpha decay occurs through quantum tunneling, where the alpha particle "tunnels" through the potential barrier of the nucleus. This phenomenon explains why alpha decay can occur even when classical physics would predict it to be impossible based on the particle's energy.
35. What is the role of the weak nuclear force in beta decay?
The weak nuclear force is responsible for beta decay. It allows for the conversion of neutrons to protons (or vice versa) by changing the flavor of quarks within nucleons. This fundamental force explains why beta decay can violate parity conservation, unlike other decay modes.
36. What is the significance of the Geiger-Nuttall law in alpha decay?
The Geiger-Nuttall law relates the decay constant (or half-life) of an alpha-emitting isotope to the energy of the emitted alpha particle. It demonstrates that isotopes emitting higher-energy alpha particles generally have shorter half-lives, providing insights into nuclear structure and stability.
37. How does the pairing effect influence nuclear stability and decay modes?
The pairing effect refers to the increased stability of nuclei with even numbers of protons and neutrons. This effect arises from the tendency of nucleons to form pairs, leading to higher binding energies. It influences decay modes and explains why odd-odd nuclei are generally less stable.
38. What is the physical basis for the exponential nature of radioactive decay?
The exponential nature of radioactive decay arises from the fact that each nucleus has a constant probability of decaying in a given time interval, regardless of its age. This leads to a decay rate proportional to the number of remaining nuclei, resulting in the characteristic exponential curve.
39. How does the concept of nuclear isomers relate to radioactive decay?
Nuclear isomers are excited states of atomic nuclei that have measurable lifetimes before decaying to their ground state. They can undergo gamma decay or other decay modes. Isomers complicate decay schemes but provide valuable information about nuclear structure and energy levels.
40. What is the significance of the "valley of stability" in the chart of nuclides?
The "valley of stability" is the region in the chart of nuclides where the most stable isotopes for each element are found. It represents the optimal neutron-to-proton ratio for nuclear stability. Nuclei far from this valley are unstable and undergo radioactive decay to approach this region.
41. How does the concept of nuclear magic numbers relate to the stability against radioactive decay?
Nuclear magic numbers (2, 8, 20, 28, 50, 82, 126) represent particularly stable configurations of protons or neutrons in a nucleus. Nuclei with magic numbers of protons or neutrons are generally more resistant to radioactive decay due to their increased binding energy and shell closure.
42. What is the role of the strong nuclear force in preventing spontaneous nuclear decay?
The strong nuclear force is the primary force holding nucleons together in the nucleus. It counteracts the electrostatic repulsion between protons and provides the binding energy that must be overcome for decay to occur. The balance between these forces determines nuclear stability.
43. How does the concept of nuclear deformation influence radioactive decay rates?
Nuclear deformation, where nuclei deviate from a spherical shape, can affect decay rates. Deformed nuclei may have different energy levels and transition probabilities compared to spherical nuclei, leading to changes in decay modes and half-lives, particularly in regions far from stability.
44. What is the significance of the "liquid drop model" in understanding nuclear stability and decay?
The liquid drop model treats the nucleus as a drop of incompressible nuclear fluid. It helps explain general trends in binding energy and provides insights into nuclear fission. While it doesn't account for shell effects, it's useful for understanding bulk properties related to decay.
45. What is the physical meaning of the decay energy (Q-value) in radioactive processes?
The decay energy or Q-value represents the energy released in a radioactive decay process. It's the difference in mass-energy between the parent nucleus and the sum of the daughter products. Positive Q-values indicate energetically favorable decays that can occur spontaneously.
46. How does the concept of nuclear deexcitation relate to gamma decay and internal conversion?
Nuclear deexcitation is the process by which an excited nucleus releases energy to reach a lower energy state. This can occur through gamma decay (emission of a high-energy photon) or internal conversion (transfer of energy to an orbital electron). The competition between these processes depends on nuclear structure.
47. What is the role of virtual particles in understanding the mechanism of radioactive decay?
Virtual particles, allowed by quantum uncertainty, mediate the forces involved in radioactive decay. For example, in beta decay, a virtual W boson mediates the weak interaction. These particles explain how forces operate over nuclear distances and contribute to decay probabilities.
48. What is the significance of the "island of stability" hypothesis in the search for superheavy elements?
The "island of stability" hypothesis suggests that certain superheavy elements with specific numbers of protons and neutrons might have unusually long half-lives. This concept drives research into synthesizing new elements and challenges our understanding of nuclear stability at extreme proton-neutron ratios.
49. How does the concept of nuclear shape coexistence affect decay modes and rates?
Nuclear shape coexistence occurs when a nucleus can exist in different shapes (e.g., spherical and deformed) at similar energies. This phenomenon can lead to complex decay schemes, isomeric states, and unexpected decay rates, particularly in regions of the nuclear chart far from stability.
50. What is the role of pairing correlations in determining the stability and decay modes of odd-A nuclei?
Pairing correlations, arising from the tendency of nucleons to form pairs, significantly affect the stability and decay modes of nuclei, especially those with odd numbers of protons or neutrons (odd-A nuclei). These correlations influence binding energies, excited states, and decay probabilities.

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