FE Other Disciplines Practice Question Solution included after investigation
CASE E-092 · FE

The Source That Fell to 30, Not 60

Eighteen hours represented three half-lives, not two. A 240-unit rate therefore fell to 30, not 60.

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Case E-092 engineering failure visual
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Inspect

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2

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3

Prove

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4

Fix

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5

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Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A radioactive source has an initial measured rate of 240 arbitrary exposure-rate units. Its half-life is 6.0 hours. A note states that after 18 hours only two half-lives have elapsed and reports 60 units remaining. Determine the correct remaining rate after 18 hours and the time required for the rate to fall below 10 units.

Safety Health Environment Other Disciplines Design Verification Root Cause Analysis Safe Correction
E-092
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

The elapsed-time interval was divided into the wrong number of half-lives.

What was missed

18 hours contains three 6-hour half-lives.

Corrected model

Use A=A0(1/2)^(t/t_half).

QUICK ANSWER

With A0=240, half-life 6 h, and t=18 h, three half-lives elapse. A=240(1/2)^3=30 units. The rate falls below 10 units after about 27.5 hours.

ENGINEERING TAKEAWAY

Use A=A0(1/2)^(t/t1/2), where the exponent is the number of elapsed half-lives.

CASE QUESTIONS

Questions this case should settle.

What is the half-life decay equation?

A=A0(1/2)^(t/t_half).

How many half-lives occur in 18 hours when the half-life is 6 hours?

Three.

NEXT FE PRACTICE QUESTION

The Relief Valve That Saw 480 N, Not 560

Safety Health Environment · 5–10 min

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WHAT YOU’LL LEARN

Real failures. Lasting skills.

Each case is designed to build the judgment, analysis, and confidence you need for engineering exams — and beyond.

  • Apply core engineering concepts to real-world problems
  • Practice structured troubleshooting and analysis
  • Strengthen exam-ready thinking through realistic scenarios
COMMON QUESTIONS
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