The Q value of a nuclear reaction A + b → C + d is defined by

Q = [ m_A + m_b– m_C – m_d]c²

Where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.

(i) ¹₁H + ³₁H → ²₁H + ²₁H

(ii) ¹²₆C + ¹²₆C → ²⁰₁₀Ne + ⁴₂He

Atomic masses are given to be

m (²₁H) = 2.014102 u

m (³₁H) = 3.016049 u

m (¹²₆C) = 12.000000 u

m (²⁰₁₀Ne) = 19.992439 u

i) The given equation is:

Hence, according to given data and given definition of Q value in the question

Q value = [m(¹H₁) + m(³H₁)-2 × m(²H₁)] × c²

= (-0.00433u × c²) =

-0.00433 × 931.5 MeV

= -4.0334 MeV

The negative value of Q value suggests this reaction is endothermic.

ii) The reaction is :

According to previous solution Q value,

Q = [2 × m(¹²C₆)-m(²⁰Ne₁₀)-m(⁴He₂)] × c²

= (0.004958u) × c²

= 0.004958 × 931.5

= 4.6183MeV

Here, the Q value is positive hence reaction is exothermic.