The Q-value of a nuclear reaction A + b `to` C + d is defined by `Q=[m_A + m_b -m_C -m_d]c^2 ` , where the masses refer to nuclear rest masses . Determine from the given data whether the following reactions are exothermic or endothermic .
(a)`._1^1H + ._1^3H to ._1^2 H ._1^2 ` , (b)`._6^12C + ._6^12C to ._10^20Ne + ._2^4He`
Atomic masses are given to be `m(._1^1H)` = 1.007825 u, `m(._1^2H)` = 2.014102 u , `m(._1^3H)` =3.016049 u, `m(._1^12C)` =12.000000 u, `m(._10^20Ne)` =19.992439 u, `m(._2^4He)` =4.002603 u

Explanation

(a)`._1^1H+._1^3H to ._1^2H + ._1^2H`
`therefore Q=m_N(._1^1H) +m_N(._1^3H) -m_N(._1^2H)-m_N(._1^2H)`
`=m(._1^1H) - m_e + m(._1^3H) -m_e -m(._1^2H) + m_e -m(._1^2H) + m_e`
`=m(._1^1H) +m(._1^3H) -m(._1^2H) - m(._1^2H)`
=1.007825 + 3.016049 - 2 x 2.014102
=-0.00433 x 931.5 MeV =-4.03 MeV
`because ` Q lt 0, the reaction is endothermic.
(b)`._6^12C + ._6^12C to ._10^20 Ne + ._2^4He`
`therefore Q=2m_N(._6^12C) -m_N(._10^20Ne) -m_N(._2^4He)`
`=2m(._6^12C) -12m_e-m(._10^20Ne) + 10m_e -m(._2^4He ) + 2m_e`
=[2 x 12.000000-19.992439-4.002603] x 931.5 MeV
=0.004958 x 931.5 MeV = 4.62 MeV
`because` Q gt 0 , so, the reaction is exothermic .