Half-Life and Rate of Decay

Half-Life and Rate of Decay MDCAT MCQs with answers

19 past paper MCQs on Half-Life and Rate of Decay, from the Nuclear Physics unit of MDCAT Physics. The year each question appeared is shown where known; tap “Show answer” for the correct option and a short solution.

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1.The half-life of strontium is 8.70 hours. Its decay constant is: (MDCAT 2022)

  1. $0.000022\ \mathrm{s^{-1}}$
  2. $45000\ \mathrm{s^{-1}}$
  3. $0.0022\ \mathrm{s^{-1}}$
  4. $0.22\ \mathrm{s^{-1}}$
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Correct answer: (a) $0.000022\ \mathrm{s^{-1}}$

$\lambda=0.693/T_{1/2}=0.693/(8.70\times3600)=2.2\times10^{-5}\ \mathrm{s^{-1}}$.

2.The unit of the decay constant is: (MDCAT 2024)

  1. m
  2. s
  3. $\mathrm{s^{-1}}$
  4. mm
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Correct answer: (c) $\mathrm{s^{-1}}$

The decay constant is the fraction decaying per unit time, so it is measured per second.

3.If we have $N_0$ atoms of a radioactive element, then after a period of $n$ half-lives the number of atoms left behind is: (MDCAT 2024)

  1. $2^{n}N_0$
  2. $(1/2)^{n}N_0$
  3. $(N_0)^{n}$
  4. $N_0/n$
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Correct answer: (b) $(1/2)^{n}N_0$

Each half-life halves the number, so $n$ of them leave $N_0/2^{n}$.

4.The half life of radium is about \$1600\$ years. If \$100\,\mathrm{g}\$ of radium exists now, \$25\,\mathrm{g}\$ will remain undecayed after: (UHS MDCAT 2017)

  1. $4800$ years
  2. $6400$ years
  3. $2400$ years
  4. $3200$ years
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Correct answer: (d) $3200$ years

A quarter is left after two half lives, so $2\times1600=3200$ years.

5.After 3 half-lives, the remaining fraction of a radioactive sample is: (UHS MDCAT 2025)

  1. 1/2
  2. 1/4
  3. 1/8
  4. 1/16
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Correct answer: (c) 1/8

Each half life halves what is left, so after three of them $1/8$ remains.

6.The time in which half of the given number of radioactive nuclei decay is known as (UHS MDCAT 2025)

  1. 1/2 life of radioactive element.
  2. 2/3 life of radioactive element.
  3. 1/4 life of radioactive element.
  4. 2/5 life of radioactive element.
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Correct answer: (a) 1/2 life of radioactive element.

That time is the half life of the element.

7.Half-life of a radioactive element is 10 days. After 30 days, fraction remaining is: (NUMS MDCAT 2025)

  1. 1/2
  2. 1/4
  3. 1/8
  4. 1/16
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Correct answer: (c) 1/8

Thirty days is three half lives, and each halves what is left, so $1/8$ remains.

8.If we have "No" number of any radioactive element then after a period of "n" half-lives the number of atoms left behind is (UHS MDCAT 2024)

  1. 2^n No
  2. (½)^n No
  3. (½ No)^n
  4. (2No)^n
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Correct answer: (b) (½)^n No

Each half life halves the number left, so after $n$ of them $(1/2)^n N_0$ remain.

9.The half-life of Iodine – 31 is: (SZABMU MDCAT 2023)

  1. 10 days
  2. 8 days
  3. 45 days
  4. 60 days
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Correct answer: (b) 8 days

Iodine-131 has a half life of about eight days.

10.The half-life of carbon is 5730 years. How much carbon will left after 22920 years? (SZABMU MDCAT 2023)

  1. 1/32nd
  2. 1/16th
  3. 1/64th
  4. 1/4th
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Correct answer: (b) 1/16th

$22920/5730$ is four half lives, and each halves what is left, leaving a sixteenth.

11.The time taken for half the number of atoms of radioactive isotopes to disintegrate is called: (NUMS MDCAT 2023)

  1. Average life
  2. Mean life
  3. Total life
  4. Half life
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Correct answer: (d) Half life

That time is the half life.

12.A 32g radioactive element decays and remains 2g after 60 days. What is half-life of this radioactive element? (NUMS MDCAT 2023)

  1. 2 days
  2. 6 days
  3. 10 days
  4. 15 days
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Correct answer: (d) 15 days

Going from $32$ to $2\,\mathrm{g}$ is four half lives, and $60/4$ is $15$ days.

13.What is the relationshlp between the half life of a radioactive isotope and its wavelength? (PMC MDCAT 2022)

  1. they are equal in magnitude
  2. they are directly proportional
  3. they are inversely proportional
  4. No relation
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Correct answer: (d) No relation

Half life is a property of the nucleus and has nothing to do with any wavelength.

14.Q.75 A 32g radioactive element decays and remains 2g after 60 days. What is the half-life of radioactive element? (NUMS MDCAT 2022)

  1. 2 days
  2. 6 days
  3. 10 days
  4. 15 days
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Correct answer: (d) 15 days

From $32$ to $2\,\mathrm{g}$ is four half lives, and $60/4$ is $15$ days.

15.What will happen in a time of 7 hours, if a radioactive substance has an average life of 7 hours? (PMC Practice 2021)

  1. Half of the active nuclei decay
  2. Less than half of the active nuclei decay
  3. More than half of the active nuclei decay
  4. Total nuclei decay
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Correct answer: (c) More than half of the active nuclei decay

The average life is longer than the half life, so more than half have gone by then.

16.C14 has a half-life of 5700 years. At the end of 11400 years, the actual amount left is? (PMC Practice 2021)

  1. 0.0625 of the original amount
  2. 0.5 of the original amount
  3. 0.25 of the original amount
  4. 0.125 of the original amount
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Correct answer: (c) 0.25 of the original amount

Eleven thousand four hundred years is two half lives, so a quarter is left.

17.There are initially 400 atoms in a radioactive sample. What would be the number of atoms after 3 half – life? (PMC MDCAT 2020)

  1. 400
  2. 200
  3. 50
  4. 25
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Correct answer: (c) 50

Three half lives leave an eighth, and $400/8$ is $50$.

18.Calculate the half life of Bismuth-214 which has a decay constant of 4.3 x 10-4 s-1: (UHS MDCAT 2018)

  1. 2.9 x 10-3s
  2. 1.6 x 10^3 s
  3. 3.9 x 103s
  4. 2.9 x 103s
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Correct answer: (b) 1.6 x 10^3 s

$t_{1/2}=0.693/\lambda=0.693/4.3\times10^{-4}$, about $1.6\times10^3\,\mathrm{s}$.

19.The relation between decay constant ‘λ’ and half-life ‘T½’ of radioactive substance is: (UHS MDCAT 2016)

  1. λ = 1/T1/2
  2. λ = 0693 T1/2
  3. λ = T1/2
  4. λ = 0.693/T1/2
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Correct answer: (d) λ = 0.693/T1/2

$\lambda=0.693/t_{1/2}$.

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