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

Q = [mA+ mb − mC − md]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.

$\ce{^12_6C + ^12_6C ->^20_10Ne + ^4_2He}$

Atomic masses are given to be

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

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

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

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

#### Solution

The given nuclear reaction is:

$\ce{^12_6C + ^12_6C ->^20_10Ne + ^4_2He}$

t is given that:

Atomic mass of "m"(""_6^12"C") = 12.0 u

Atomic mass of "m"(""_10^20"Ne") = 19.992439 u

Atomic mass of "m"(""_2^4"He") = 4.002603 u

The Q-value of this reaction is given as:

"Q" = [2"m"(""_6^12"C") - "m"(""_10^20"Ne") - "m"(""_2^4"He")]"c"^2

= [2 xx 12.0 - 19.992439 - 4.002603]"c"^2

= (0.004958 c^2)"u"

= 0.004958 xx 931.5 = 4.618377 MeV

The positive Q-value of the reaction shows that the reaction is exothermic.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 13 Nuclei
Exercise | Q 13.15 (ii) | Page 463
NCERT Class 12 Physics Textbook
Chapter 13 Nuclei
Exercise | Q 15.2 | Page 463

Share