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Question #77896

Difficulty: 8/10 | 🟢 Free

The Question

A stationary nucleus $P$ undergoes spontaneous fission into two nuclei $Q$ and $R$ according to the reaction $P \rightarrow Q + R$ . The rest masses of the nuclei are measured as $m_P = 238.050 \text{ u}$ , $m_Q = 144.12 \text{ u}$ , and $m_R = 93.682 \text{ u}$ . The energy equivalent of $1 \text{ u}$ is given as $931.5 \text{ MeV}/c^2$ . Four students calculate the $Q$ -value of this reaction. Due to various misapplications of the rules of significant figures, they obtain different results. All of the following values represent INCORRECT calculations of the $Q$ -value, EXCEPT:

Options

A.
$231 \text{ MeV}$
B.
$233 \text{ MeV}$
C.
$2.3 \times 10^2 \text{ MeV}$
D.
$231.0 \text{ MeV}$

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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

Examiner Levers

Negative Thinking

Uses "NOT", "EXCEPT", or "INCORRECT" to flip the logic gate.

Difficulty Boost : +2

Concept Bridge

Cross-chapter synthesis (e.g., using Logarithms in Electrochemistry).

Difficulty Boost : +5

Common Mistakes

This question tests the sequential application of significant figure rules during a multi-step calculation, specifically the critical transition from addition to multiplication.

Students commonly fall into the trap of either not rounding the intermediate mass defect to the correct number of decimal places (yielding 0.248 u and incorrectly arriving at 231 MeV) or failing to recognize that the properly rounded mass defect (0.25 u) now dictates a strict 2-significant-figure limit for the final multiplication, incorrectly keeping 3 or 4 significant figures (yielding 233 MeV or 232.9 MeV).

It punishes the assumption that intermediate values retain infinite precision.

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	8
Target Solve Time	180 sec
Access	Free