Half-Life Models & Nuclear Equations — Practice · Grade 11 Science

Chapter: Redox, Cells & Nuclear Chemistry

What this practice covers

By the end of Half-Life Models & Nuclear Equations you should be able to:

8 questions, numeric and written answer, each with a worked explanation.

Vocabulary used: activity, daughter nucleus, decay constant.

Problem 1

80 g parent undergoes two half-lives. Find parent mass.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

20 g

80/4=20.

Problem 2

Does all parent disappear after two half-lives?
Answer and explanation

No. One-quarter remains on average in a large population.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 3

120 g parent undergoes three half-lives. Find remaining parent.
Hints

List the given quantities, select a relationship, and check units before substituting.

Answer and explanation

15 g

120/8=15.

Problem 4

What changes in beta-minus decay?
Answer and explanation

A neutron becomes a proton, an electron and an antineutrino are emitted; Z increases 1 and A stays the same.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 5

A parent fraction is 1/16 with half-life 2 days. Find elapsed time. Show the reasoning, not just the conclusion.
Hints

A half-life is repeated fractional decrease, not fixed mass loss.

Answer and explanation

Four half-lives, so 8 days.

Problem 6

If initial count is 1000 and decay constant is ln2/4 h⁻¹, find count after 8 h using N=N₀e⁻λt.
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

1000e⁻²ln2=250, equivalent to two half-lives.

Problem 7

Logarithms extend the model beyond whole half-life stepsLogarithms extend the model beyond whole half-life stepsN/N₀ = 0.30; t½ = 10.0 dayst = t½ × ln(N/N₀) / ln(1/2)t ≈ 17.4 daysA fractional number of half-lives is physically meaningful.
Original selected 30% remaining example with a hypothetical ten-day half-life; not an age estimate for a historical object.
Interpret the supplied visual. Why is the time positive when both logarithms in the selected expression are negative?
Answer and explanation

Their ratio is positive; the parent fraction has fallen below one over a positive time interval.

A measured parent fraction need not be a simple power of one half. Rearrange the exponential using logarithms to solve t=t½ ln(N/N₀)/ln(1/2). Both the fraction and logarithm arguments are dimensionless. A fraction between zero and one gives positive time because numerator and denominator are both negative. Dating requires an appropriate initial inventory or calibrated initial ratio and a sufficiently closed accounting system; contamination or material exchange can invalidate a simple age inference.

Their ratio is positive; the parent fraction has fallen below one over a positive time interval.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the chemistry relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 8

A modeled isotope has t½=8.00 days. Comparable initial net signal is 800 counts/min. Later gross signal is 250 and matched background 50 counts/min. Find remaining fraction and modeled elapsed time, naming one assumption.
Answer and explanation

Later net signal=200, so fraction=200/800=0.250. That is two half-lives, giving 16.0 days. Assume stable geometry/efficiency and a net signal proportional to the same parent population with an appropriate closed account.

Later net signal=200, so fraction=200/800=0.250. That is two half-lives, giving 16.0 days. Assume stable geometry/efficiency and a net signal proportional to the same parent population with an appropriate closed account.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the chemical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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