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Question #42000

Difficulty: 8/10 | 🟢 Free

The Question

A heavy nucleus $X$ undergoes spontaneous fission into two fragments $Y$ and $Z$ according to the reaction $X \rightarrow Y + Z$ . The atomic masses are given as $m_X = 236.053 \text{ u}$ , $m_Y = 140.91 \text{ u}$ , and $m_Z = 94.949 \text{ u}$ . Taking the energy equivalent of $1 \text{ u}$ to be $931.5 \text{ MeV}$ , calculate the $Q$ -value of the reaction. Express your final answer with the correct number of significant figures.

Options

A.
$1.8 \times 10^2 \text{ MeV}$
B.
$1.81 \times 10^2 \text{ MeV}$
C.
$1.77 \times 10^2 \text{ MeV}$
D.
$1.807 \times 10^2 \text{ MeV}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Significant Figures in Mixed Operations|Nuclear Fission Energy Balance

Why This Question Is Tricky

Common Mistakes

This question tests the propagation of significant figures through mixed operations (addition followed by multiplication) in a standard nuclear physics context.

Students often fail to realize that the subtraction of masses ( $m_X - m_Y - m_Z$ ) follows the 'least precise decimal place' rule, which drastically reduces the number of significant figures from five or six down to just two.

Consequently, when multiplying by the conversion factor ( $931.5 \text{ MeV/u}$ ), the final energy must be restricted to two significant figures.

A common trap is treating the intermediate mass defect as having three significant figures ( $0.194$ ) or keeping the precision of the conversion factor, leading to incorrect rounding.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Units and Measurements - Class 11 Part 1
Concept	Significant Figures in Mixed Operations
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free