Download Nuclear - PEO Scarborough Chapter

RADIOACTIVITY AND NUCLEAR SCIENCE
Kevin George, EIT
Alpha, Beta and Gamma Decay
Atoms are the smallest particles of matter and are made of protons, neutrons, and electrons. At
the centre of the atom is a very small region called a nucleus. The nucleus houses protons and
neutrons. The electrons form a cloud around the nucleus. The neutrons hold mass containing
particles (protons) together in the nucleus. When an atom has too much energy, it dissipates
energy through emission of alpha (α), beta (β) and gamma (γ) radiation. This phenomenon is
called radioactivity or radioactive decay.
Heavy unstable elements give away two protons and neutrons to attain stability. This
phenomenon is called alpha decay. For example, uranium (U) undergoes alpha decay to form
thorium (Th), as depicted in Figure 1, according to the following equation:
238
→ 90Th234+2He4
92U
FIGURE 1: ALPHA DECAY OF A URANIUM-238 NUCLEUS
In beta decay, a neutron is converted into a proton and a high velocity electron is ejected to attain
atomic stability. There are two types of beta decay:
1. Positive - release of positively charged particle called positron and neutrino
2. Negative - release of negatively charged particle called electron and antineutrino.
For example, carbon-14 (an unstable isotope of carbon), when subjected to beta decay, forms
nitrogen (stable) along with an electron;
14
6C
→ 7N14 + -1β0
Gamma radiation is the simplest form of radiation. It usually occurs soon after an alpha or beta
decay. The nucleus undergoes many energy fluctuations and strenuous activity during α and β
decay and somehow wants to let off some ‘steam’! The easiest way for the nucleus to do this is to
eject a gamma burst. Gamma rays are electromagnetic rays and not a particle, thus the atomic
number (Z) and mass number (A) remain the same. The atomic number is the number of protons
in an element, and the mass number is the number of protons plus the number of neutrons.
PEOSC – STEMZ
1
Source: Boundless. “Atomic Number and Mass Number.” Boundless Chemistry. Boundless, 08
Aug. 2016. Retrieved 29 Oct. 2016 from
In general, a gamma decay is characterized as follows:
ZX
*
A
→
ZX
A
+ 0γ0
FIGURE 2: ILLUSTRATION OF GAMMA DECAY
The table below summarizes the three types of radioactive decay.
Type
α
β
γ
Nature
Weight
Electrical Charge
Two neutron and two Four times the mass of
+2 (twice that of a proton)
protons
proton or neutron
About 1/2000 the mass of ±1 (same strength as of an
One electron
single proton or neutron
electron)
High energy form of
No mass
No charge
light
Rutherford-Soddy Law and Half-Life
Rutherford-Soddy Law states that “At any instant, the rate of decay of radioactive atoms is
proportional to the number of atoms present at that instant”. If N is the number of radioactive
atoms present at any instant, then the rate of decay is given by λ-decay constant or disintegration
constant. Also, at t=0, N=N0. On solving further, we obtain
N=N0e-t
–dN/dt N or –dN/dt = N
The time interval in which the mass of a radioactive substance or the number of its atoms is
reduced to half of its initial value is called half-period or half-life of that substance.
We know that N=N0e-λt and by definition, N=N0/2
And, N0/2 = N0 e-λT
∴ Half-life,
T1/2=0.693/
Sources
Ernest Z. (2014). What is the nuclear equation for uranium-238 after alpha radiation is emitted?
Socratic.org. Retrieved on January 6, 2016 from http://socratic.org/questions/what-is-thenuclear-equation-for-uranium-238-after-alpha-radiation-is-emitted
PEOSC – STEMZ
2
Retrieved on January 6, 2016 from http://ilabsteacher.sesp.northwestern.edu/labjournal/journal/preview/285/
Karam, P.A. and Stein, B.P. (2009). SCIENCE FOUNDATIONS Radioactivity. New York:
Infobase Publishing
Sample Questions
Q1. A certain element has half-life period of 30-days. Find its average life and disintegration
constant.
Sol: Given, T1/2 = 30 days
⇒0.693/λ = 30 days
⇒1/λ = 43.3 days = τ
⇒and λ = 0.023 day-1
Q2. Find the half-life period of a radioactive material if its activity drops to (1/16)th of its initial
value in 40 years.
Sol: We know that:
N/N0 = (1/2)n = (1/16) (given)
∴n = 4
Also, T1/2 = t/n = 40/4 = 10 years
Q3. What is the activity of 1 gram of Radium-226 having half-life of 1600 years?
Sol: λ = 0.693/T1/2
= 1.35x10-11 sec-1
There are 226g of Radium/mole and each mole has 6.02x1023 nuclei. Thus, in 1g there are
2.66x1021 nuclei.
∴ Activity, λN = 3.6x1010 decays/sec
Q4. Strontium is chemically similar to calcium and can replace calcium in bones. The radiation
from Sr90 can damage bone marrow where blood cells are produced, and lead to serious health
problems. How long would it take for all but 0.01% of a sample of Sr90 to decay? ( λ=0.024 year-1
)
Sol: Let’s assume initial mass M0=1 and final mass, Mf = 0.01% of M0
From the radioactive decay law,
Mf = M0 e-λt
∴t = 383.4 years
Q5. When 92U238 decays to 82Pb206, what are the number of alpha and beta particles emitted?
Sol: Difference of atomic masses
=238-206=32
Total number of alpha particles emitted=32/4= 8
∴ atomic number decreases by 8x2=16
the atomic number should become 91-16=76, but the atomic number is 82.
∴ 6β- particles are emitted
PEOSC – STEMZ
3
8 alpha & 6 beta particles emitted
Q6. In the series 92U238 → X → ZYA , what is the value of Z and A if the first disintegration is an α
decay and the next is a β- ?
Sol: Z = 91, A = 234
Q7. The decay constant of a radioactive substance is 1 month-1. What percentage of the
substance will decay in two months?
Sol: T1/2 = 0.693 months
N/N0 = (1/2)2/0.693 = 0.135
And, 100 x [N0 – N]/N0
= 100 x [N0 – 0.135N0]/N0
≈ 86%
10
MeV
Fission
PEOSC – STEMZ
200
Mev
4