# The Q value of a nuclear reaction \\ce{A + b → C + d}\ is defined by Q = [ mA+ mb− mC− md]c2 where the masses refer to the respective nuclei. - Physics

Numerical

The Q value of a nuclear reaction $\ce{A + b → C + d}$ is defined by

Q = [ mA+ mb− mC− md]cwhere 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.

$\ce{^1_1H + ^3_1H -> ^2_1H + ^2_1H}$

Atomic masses are given to be

"m"(""_1^2"H") = 2.014102 u

"m"(""_1^3"H") = 3.016049 u

"m"(""_6^12"C") = 12.000000 u

"m"(""_10^20"Ne") = 19.992439 u

#### Solution

The given nuclear reaction is:

$\ce{^1_1H + ^3_1H -> ^2_1H + ^2_1H}$

It is given that:

Atomic mass m(""_1^1"H") = 1.007825 u

Atomic mass m(""_1^3"H") = 3.016049 u

Atomic mass m(""_1^2"H") = 2.014102 u

According to the question, the Q-value of the reaction can be written as:

Q = ["m"(""_1^1"H") + "m"(""_1^3"H") - 2"m"(""_1^2"H")]"c"^2

Q = (- 0.00433 c2)u

But 1 u = 931.5 MeV/c2

= [1.007825  + 3.016049 - 2 xx 2.014102]c^2

"Q" = - 0.00433 xx 931.5 = - 4.0334 MeV

The negative Q-value of the reaction shows that the reaction is endothermic.

Concept: Law of Radioactive Decay
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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 13 Nuclei
Exercise | Q 13.15 (i) | Page 463
NCERT Class 12 Physics Textbook
Chapter 13 Nuclei
Exercise | Q 15.1 | Page 463

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