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# Alpha Decay: Definition, Examples, Practice Problems and FAQs

• What is Alpha Decay?
• Momentum Conservation in Alpha Decay
• Practice Problems of Alpha Decay
• FAQs of Alpha Decay

## What is Alpha(α) Decay?

• An alpha particle is an energetic He - nucleus(2He4) with atomic number 2 and mass number 4. It carries a positive charge of +2e.
• Alpha particles are emitted when heavy elements like Uranium U-235 undergo radioactive decay.
• During an decay, the atomic number decreases by 2 and the mass number decreases by 4. Consider an element ZXA whose atomic number is Z and mass number is A. Upon undergoing - decay, it transforms to a daughter nucleus Y. The reaction can be represented as,

ZXA ━━━⟶  Z-2YA-4 + 2He4

Mass of the parent nucleus, m = m( ZXA) - Zme

Mass of the daughter nucleus, mY = m( Z-2YA-4) - (Z - 2)me

Mass of the alpha particle mα = m ( 2He4) - 2me, m- mass of the electron in amu.

The energy liberated during a nuclear reaction is called its Q-value. The  Q- value of the - decay can be calculated as,  c- velocity of light.

• >The energy released is available as kinetic energy to the products.
• Example of an  - decay:   92U238 decays to Thorium  90Th234 emitting an α - particle.

92U238  ━━━⟶  90Th234 + 2He4

• It is the phenomenon through which unstable nuclei become stable by emitting an α particle or β particle. Sometimes, electromagnetic radiations called gamma () rays are produced.
• A β - particle is essentially a positron e+ or an electron e-.
• Radioactivity is a nuclear phenomenon. The phenomenon of α, β or γ radiation depends upon the size of the nucleus undergoing decay and not on other factors like temperature, pressure or other physical conditions.

## Momentum Conservation in Alpha Decay

The total momentum is conserved in an alpha decay reaction. Let pi indicate initial momentum and pf indicate the final momentum. Since the parent nucleus is at rest, pi=0.

ZXA  ━━━⟶  Z-2YA-4 + 2He4

Let m indicate the mass of the -particle and my- mass of the daughter nucleus. Let v indicate the recoil velocity of the -nucleus and vy indicate the velocity of the daughter nucleus. Then final momentum p= mαvα-myvy

Since p= pi; mαvα - myv= 0 ⇒ mαvα = myvy

The α- particle moves in the direction opposite to that of the daughter nucleus.

## Practice Problems of Alpha Decay

Q1) Complete the following reaction

88Ra226  ━━━⟶  86Rn222 + ?

Solution) Since there is a decrease in atomic number by 2 and mass number by 4, the above reaction is an - decay.

⇒ 2He4 is emitted in the process.

∴  88Ra226  ━━━⟶  86Rn222 2He4

Q2) The total number of  and  particles emitted in the following nuclear reaction is:

92U238  ━━━⟶  82Pb214 is

1. 6          (b) 8       (c) 7     (d) 10

Solution) b

92U238  ━━━⟶  82Pb214 + 6 2He+ 2e-1

No. of alpha particles = 6

No. of beta particles = 2

Q3) A nucleus having a mass number of 220, initially at rest, emits an α - particle. If the Q - a value of the reaction is 5.5 MeV, then the energy of the α - particle will be

(a) 4.8 MeV (b)5.4 MeV ( c ) 5.5 MeV (d)6.8 MeV

Solution) b

Let X   ━━━⟶  Y+ 2He4

Given, mass of X = 220

∴ Mass of Y = 220 - 4 = 216

Let K1 be the kinetic energy of Y and K2 be the kinetic energy of the  2He4 nucleus.

Then K+ K= 5.5 MeV -- (i)

Now linear momentum  , hence momentum p1 of Y can be written as

And linear momentum of particle can be written as p2

Since momentum is conserved ; p1=p2

=54 ; K2=54 = K-- (ii)

Solving (i) and (ii), we get K= 5.4 MeV.

Q4) Alpha particles emitted from a radioactive substance are

(a)Ionized hydrogen nuclei

(b)Doubly ionized helium atom

(c)Uncharged particles having mass equal to proton

(d)negatively charged particles

Solution)

Alpha particles are doubly ionized helium atoms.

## FAQs of Alpha Decay

Question 1. Heavy nuclei like uranium do not undergo β - decay. Why?

Answer. Heavy nuclei like Uranium undergo α - decay. β - decay occurs in lighter nuclei which have excess protons or neutrons

Question 2. Write the - decay reaction of  88Ra226?