Fundamentals of Alpha & Beta Emission- Gamma Decay, Beta Decay, Alpha Decay, Practice Problems, FAQs

Have you heard of Little Boy or Fat Man? These are nicknames of two atom bombs that were dropped on Japan in 1945. The bombs killed and crippled hundreds of thousands of people, and the effects are witnessed even today.

These killer bombs were believed to have killed approximately 140,000 people in Hiroshima and an additional 74,000 in Nagasaki, both in Japan. Many of the survivors would go on to develop leukaemia, cancer, or other horrific radiation-related side effects in the years that followed.

So, what is so special in these bombs which are causing destruction after 77 years also? They contained the Radioactive element Uranium which emits radiation or does some decay like alpha decay, beta decay and gamma decay. Let's discuss them in detail.

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Table of Contents

Fundamentals of Alpha & Beta emission
Gamma-Decay
Beta-Decay
Alpha Decay
Practice Problems
Frequently Asked Questions

Fundamentals of alpha & beta emission

Are the terms radioactivity and radioactive decay, familiar to you?

If not, let us first define what it is. Nuclear instability causes radioactivity to occur in the nuclei of atoms. Historically, a little amount of uranium compound was wrapped in black paper and stored in a drawer alongside photographic plates. An examination of these plates later indicated that they had been exposed. This phenomenon was referred to as "radioactive decay."

Some elements constantly dissolve from their parent elements in an attempt to stabilise themselves by emitting large amounts of energy in the form of radiation and turning into a different element.

By chance, Henry Becquerel discovered radioactivity. There are basically three decays which occur to stabilise a radioactive atom. These are

Gamma Decay and Emission (Photons having high energy are emitted)
Beta Decay and Emission (Emission consists of Electrons)
Alpha Decay and Emission (Emission consists of Helium nucleus)

All these are ionizing radiations, that can knock out neutral atoms into ions. Depending upon their mass and energy their effect varies. Alpha particles can cause damage by their charge and mass but will be stopped by a piece of paper on its way. Beta particles move with more kinetic energy and can be stopped by a thin sheet of aluminium. Gamma rays are the most energetic and need about 6cm thick lead material to protect us from them.

Gamma-Decay

This refers to the emission of high-energy electromagnetic radiations, from the radioactive nuclei. The

-ray emission of a radioactive atom has no effect on its atomic weight or number. As a result, its position in the periodic table stays unchanged. Radiation is followed by either emission or emission in natural radioactivity.

Beta-decay

Beta () decay is of three types, corresponding to either electron emission or positron emission or Electron capture (also referred to as inverse beta decay) from lower orbitals into the nucleus..
The positron (+1e0), the electron's antimatter, has the same mass as it but the opposite charge.
The electrons and positrons emitted during - decay does not directly escape the nucleus.
Photons are produced at the moment of emission in the same way that they are released when an electron shifts from a higher energy level to a lower energy level.
Electron emission occurs when the neutron to proton ratio in the nucleus is much larger.
Positron emission occurs when the neutron to proton ratio in the nucleus is much lower.
During beta decay, the conversion of proton to neutron or neutron to proton takes place. This makes the daughter element have a group displacement of the daughter element from the parent element.

For beta, particles

Consider the element ZXA, whose mass number is A and atomic number Z. It changes into a daughter nucleus Y after decaying.

$_{Z} X^{A} ⬚ Z + 1 Y A + ⬚ + 1 e 0$

Mass of the parent nucleus, $m_{X} = m (_{Z} X^{A}) - Z m_{e}$

Mass of the daughter nucleus, $m_{Y} = m (_{Z + 1} Y^{A}) - (Z + 1) m_{e}$

Mass of the beta particle $m_{α} = m (⬚ + 1 e 0) + m e = 2 m e$ , me- the mass of the electron in amu.

Example of a - decay: $β - d e c a y :_{92} U^{238} d e c a y s t o_{93} {N p}^{238} e m i t t i n g a β - p a r t i c l e .$

$U^{238}_{93} {N p}^{238} + ⬚ + 1 e 0$

Alpha decay

An alpha particle is an energetic He-nucleus (2He4) with mass number 4 and atomic number 2. It has a positive charge of +2e.
When heavy materials, such as uranium U-235, decay radioactively, alpha particles are emitted.
During decay, the atomic number decreases by two and the mass number decreases by four.

For alpha particle

Consider the element ZXA, whose mass number is A and atomic number Z. It changes into a daughter nucleus Y after decaying.

$_{Z} X^{A} ⬚ Z - 2 Y A - 4 + ⬚ 2 H e 4$

Mass of the parent nucleus, $m_{X} = m (_{Z} X^{A}) - Z m_{e}$

Mass of the daughter nucleus, $m_{Y} = m (_{Z - 2} Y^{A - 4}) - (Z - 2) m_{e}$

Mass of the alpha particle $m_{α} = m (_{2} {H e}^{4}) - 2 m_{e}$ , me- a mass of the electron in amu.

Example of a - decay: $α - d e c a y :_{92} U^{238} d e c a y s t o T h o r i u m_{90} {T h}^{234} e m i t t i n g a α - p a r t i c l e .$

$_{92} U^{238}_{90} {T h}^{234} + ⬚ 2 H e 4$

Practice Problems

1. A mass number of A and an atomic number of Z are given for the element112Cn285. After alpha decay, it transforms into a daughter nucleus, Y. Determine Y

₁₁₀Cn²⁸¹
₁₁₃Np²⁸⁵
₁₁₄Fl²⁸⁹
₁₁₀Ds²⁸¹

Solution: ₁₁₂Cn²⁸⁵ decays to₁₁₀Ds²⁸¹ emitting a - particle because, during a decay, the atomic number decreases by two and the mass number decreases by four. Hence, the correct answer is option (D).

$⬚ 112 C n 285 ⬚ 110 D s 281 + ⬚ 2 H e 4$

2. A mass number of A and an atomic number of Z are given for the element84Po209. After beta decay, it transforms into a daughter nucleus, Y. Determine Y

₈₅At²⁰⁹
₈₂Pb²⁰⁷
₈₃Bi²⁰⁹
₈₅Po²⁰⁹

Solution: ₈₄Po²⁰⁹ decays to₈₅At²⁰⁹ emitting a - particle because, during this decay, the atomic number increases by one and the mass number remains same. Hence, the correct answer is option (A).

$⬚ 84 P o 209 ⬚ 85 A t 209 + ⬚ + 1 e 0$

3. A mass number of A and an atomic number of Z are given for the element86Rn222. After beta decay, it transforms into a daughter nucleus, Y. Determine Y

₈₄Po²¹⁸
₈₇Fr²²²
₈₇Rn²²²
₈₆Rn²²²

Solution: ₈₆Rn²²² decays to₈₇Fr²²² emitting a - particle because, during this decay, the atomic number increases by one and the mass number remains same. Hence, the correct answer is option (B).

$⬚ 86 R n 222 ⬚ 87 F r 222 + ⬚ + 1 e 0$

4. A mass number of A and an atomic number of Z are given for the element106Sg269. After alpha decay, it transforms into a daughter nucleus, Y. Determine Y

₁₀₇Bh²⁶⁹
₁₀₈Hs²⁷³
₁₀₈Hs²⁶⁵
₁₀₄Rf²⁶⁵

$⬚ 106 S g 269 ⬚ 104 R f 265 + ⬚ 2 H e 4$

Frequently Asked Questions

1. Name a few radioactivity applications.
Answer: Here are a few radioactive applications:

It is used in residential smoke detectors.

It is used to sterilise medical equipment.

It is used to detect and treat disorders.

It is used to produce power.

2. Which radioactive decay is the most dangerous?
Answer: Alpha particles are the most dangerous internal threat when compared to beta and gamma particles. Ingestion, inhalation, absorption, and injection are the most dangerous means of exposure to radioactive materials that emit alpha and beta particles. Gamma radiation is the most dangerous external threat.

3. What is the source of radioactive decay?
Answer: It all comes down to thermodynamics. Every atom tries to be the most stable possible. In the case of radioactive decay, instability develops when the number of protons and neutrons in the atomic nucleus is imbalanced. To put it simply, there is too much energy inside the nucleus to hold all of the nucleons together.

4. What Is the Distinction Between Natural and Man-Made Radioactivity?
Answer: Natural radioactivity is radiation that occurs naturally, whereas artificial radioactivity is radioactivity that is created by man-made techniques.