Question

A nucleus with mass number 220 initially at rest emits an α-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the α-particle

A) 4.4 MeV
B) 5.4 MeV
C) 5.6 MeV
D) 6.5 MeV

Answer 1

Given:

The mass no of nucleus, A = 220

The heat energy released, Q = 5.5 MeV

To Find:

The kinetic energy of the α-particle .

Calculation:

- The value of Kinetic Energy of α-particle can be calculated by the formula:

K$_{He}$ = {(A - 4) /A} × Q

⇒ K$_{He}$ = {(220 - 4) /220} × 5.5

⇒ K$_{He}$ = {216/ 220} × 5.5

⇒ K$_{He}$ = 5.4 MeV

- Hence, the correct answer for the kinetic energy of the α-particle is (B) 5.4 MeV.

Answer 2

Explanation:

Given A nucleus with mass number 220 initially at rest emits an α-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the α-particle.  If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the α-particle

• Given mass number as 220 initially at rest emits an alpha particle. We need to calculate the kinetic energy of the alpha particle.
• Now the Q value will be K.E of products – K.E of reactants
•         We heve Q = K.E (nucleus) + K.E (α-particle) – 0
•                     5.5 = K.E n + K.E α ---------- 1
• Now initially conserving linear momentum was at rest so it will be 0
• Therefore p (nucleus) + p (α-particle) = 0
•       So pn = pα
•                 So √2 x mass no (K.E) n = √2 x 4 (K.E) α (mass number of αparticle = 4)  
•                      √2 x 220 (K.E)n = √2 x 4 (K.E) α
•                           220 (K.E) n = 4 (K.E)α
•                        (K.E) α = 220 / 4 (K.E) n
•                  (K.E) α = 55 (K.E) n -------------2
• So kinetic energy of α particle is 55 times of kinetic energy of nucleus.
• Substituting in equation 1 we get
•       (K.E) n + 55 (K.E) n = 5.5
• So (K.E) n = 5.5 / 56 Mev
•                   = 0.098 Mev
• Therefore (K.E) α particle = 55 (K.E) n
•                                              = 55 x 0.098
•                                             = 5.394 Mev
•                                              = 5.4 Mev
• So kinetic energy of α particle will be 5.4 Mev

Reference link will be

https://brainly.in/question/2114573