JEE Chemistry Nuclear Chemistry MCQs Set 04

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Explore reliable objective questions for Nuclear Chemistry tailored for JEE learners. Utilizing these Chemistry multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Chapter-wise Objective Questions: Nuclear Chemistry

Navigate directly to the 50 objective questions for Nuclear Chemistry using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: The half-life of \( {}^{210}_{83}\mathrm{Bi} \) is 5 days. Starting with 20 g of this isotope, the amount remaining after 15 days is
(a) 10 g
(b) 5 g
(c) 2.5 g
(d) 6.66 g
Show Answer & Explanation

Answer: (c) 2.5 g

Explanation:
1. 15 days = 3 half-lives.
2. 20 g \( \to \) 10 g \( \to \) 5 g \( \to \) 2.5 g.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 2: 75% of a first order reaction was completed in 32 minutes. The time taken for 50% completion is
(a) 24 minutes
(b) 16 minutes
(c) 8 minutes
(d) 4 minutes
Show Answer & Explanation

Answer: (b) 16 minutes

Explanation:
1. 75% completion means two half-lives (100 \( \to \) 50 \( \to \) 25 percent left).
2. So \( t_{1/2}=32/2=16 \) minutes.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 3: The half-life of \( {}^{201}_{82}\mathrm{Pb} \) is 8 hours. Starting from one milligram of this isotope, the amount that remains after 24 hours is
(a) \( \frac12 \) mg
(b) \( \frac13 \) mg
(c) \( \frac18 \) mg
(d) \( \frac14 \) mg
Show Answer & Explanation

Answer: (c) \( \frac18 \) mg

Explanation:
1. 24 h = 3 half-lives, so the fraction left is \( (1/2)^3=1/8 \).

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 4: Radium has atomic mass 226 and a half-life of 1600 years. The number of disintegrations produced per second from 1 g is
(a) \( 4.8\times10^{10} \)
(b) \( 9.2\times10^{6} \)
(c) \( 3.7\times10^{10} \)
(d) zero
Show Answer & Explanation

Answer: (c) \( 3.7\times10^{10} \)

Explanation:
1. N = \( 6.022\times10^{23}/226=2.66\times10^{21} \) atoms.
2. λ = 0.693/(1600 \( \times \) \( 3.156\times10^7 \) s) = \( 1.37\times10^{-11}\ s^{-1} \).
3. Activity = λN = \( 3.65\times10^{10} \) disintegrations per second, about \( 3.7\times10^{10} \) (1 curie).

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 5: The half-life of a radioactive element is 6 months. The time taken to reduce its original concentration to its 1/16 value is
(a) 1 year
(b) 16 years
(c) 2 years
(d) 8 years
Show Answer & Explanation

Answer: (c) 2 years

Explanation:
1. 1/16 = \( (1/2)^4 \), so 4 half-lives = 24 months = 2 years.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 6: For a radioisotope, the value of \( T_{1/2} \) and λ are identical in magnitude. The value is
(a) 0.693
(b) \( (0.693)^{1/2} \)
(c) 1/0.693
(d) \( (0.693)^2 \)
Show Answer & Explanation

Answer: (b) \( (0.693)^{1/2} \)

Explanation:
1. \( T_{1/2}=0.693/\lambda \).
2. If \( T_{1/2}=\lambda \) then \( \lambda^2=0.693 \), so \( \lambda=(0.693)^{1/2} \).

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 7: The half-life of a radioactive substance which disintegrates by 75% in 60 minutes will be
(a) 120 min
(b) 30 min
(c) 45 min
(d) 20 min
Show Answer & Explanation

Answer: (b) 30 min

Explanation:
1. 75% decay means 2 half-lives in 60 min, so the half-life is 30 min.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 8: 87.5% decomposition of a radioactive substance is complete in 3 hours. What is the half-life of that substance?
(a) 2 hours
(b) 3 hours
(c) 90 minutes
(d) 1 hour
Show Answer & Explanation

Answer: (d) 1 hour

Explanation:
1. 87.5% decayed leaves 12.5% = 1/8 = \( (1/2)^3 \).
2. Three half-lives take 3 h, so the half-life is 1 hour.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 9: Given that a radioactive species decays according to the exponential law \( N=N_0e^{-\lambda t} \), its half-life is
(a) \( \lambda \)
(b) \( N_0 \)
(c) \( \lambda/\ln2 \)
(d) \( \ln2/\lambda \)
Show Answer & Explanation

Answer: (d) \( \ln2/\lambda \)

Explanation:
1. At \( t=t_{1/2} \), \( N=N_0/2 \), so \( e^{-\lambda t}=1/2 \) and \( t_{1/2}=\ln2/\lambda \).

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 10: The half-life of a radioactive disintegration (A \( \to \) B) with rate constant \( 231\ s^{-1} \) is
(a) \( 3.0\times10^{-2}\ s \)
(b) \( 3.0\times10^{-3}\ s \)
(c) \( 3.3\times10^{-2}\ s \)
(d) \( 3.3\times10^{-3}\ s \)
Show Answer & Explanation

Answer: (b) \( 3.0\times10^{-3}\ s \)

Explanation:
1. \( t_{1/2}=0.693/231=3.0\times10^{-3}\ s \).

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 11: The amount of \( {}^{128}_{53}\mathrm{I} \) (\( t_{1/2}=25 \) minutes) left after 50 minutes is
(a) one-half
(b) one-third
(c) nothing
(d) one-fourth
Show Answer & Explanation

Answer: (d) one-fourth

Explanation:
1. 50 min = 2 half-lives, so \( (1/2)^2=1/4 \) is left.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 12: If 3/4 of the quantity of a radioactive element disintegrates in two hours, its half-life would be
(a) 1 hour
(b) 45 minutes
(c) 30 minutes
(d) 15 minutes
Show Answer & Explanation

Answer: (a) 1 hour

Explanation:
1. 3/4 decayed leaves 1/4 = 2 half-lives in 2 hours, so the half-life is 1 hour.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 13: A certain nuclide has a half-life of 25 minutes. If one starts with 100 g of it, how much of it will remain at the end of 100 minutes?
(a) 1.0 g
(b) 4.0 g
(c) 6.25 g
(d) 12.50 g
Show Answer & Explanation

Answer: (c) 6.25 g

Explanation:
1. 100 min = 4 half-lives.
2. Amount left = 100/16 = 6.25 g.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 14: The decay constant of \( {}^{226}_{88}\mathrm{Ra} \) is \( 1.37\times10^{-11}\ s^{-1} \). A sample of radium-226 having an activity of 1.5 millicurie will contain how many atoms? (1 Ci = \( 3.7\times10^{10} \) dis/s)
(a) \( 4.1\times10^{18} \)
(b) \( 3.7\times10^{17} \)
(c) \( 2.05\times10^{15} \)
(d) \( 4.7\times10^{10} \)
Show Answer & Explanation

Answer: (a) \( 4.1\times10^{18} \)

Explanation:
1. Activity = \( 1.5\times10^{-3}\times3.7\times10^{10}=5.55\times10^{7} \) dis/s.
2. N = A/λ = \( 5.55\times10^7/1.37\times10^{-11}=4.05\times10^{18}\approx4.1\times10^{18} \).

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 15: The half-life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is
(a) 3.125 g
(b) 2.084 g
(c) 1.042 g
(d) 4.167 g
Show Answer & Explanation

Answer: (a) 3.125 g

Explanation:
1. 24 h = 6 half-lives.
2. 200/64 = 3.125 g.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 16: An artificial radioactive isotope gave \( {}^{14}_{7}\mathrm{N} \) after two successive \( \beta \)-particle emissions. The number of neutrons in the parent nucleus must be
(a) 9
(b) 14
(c) 5
(d) 7
Show Answer & Explanation

Answer: (a) 9

Explanation:
1. Two beta emissions raise Z by 2 without changing A, so the parent had Z = 5 and A = 14.
2. Neutrons = 14 - 5 = 9.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 17: If the half-life of an isotope X is 10 years, its decay constant is
(a) \( 6.932\ yr^{-1} \)
(b) \( 0.6932\ yr^{-1} \)
(c) \( 0.06932\ yr^{-1} \)
(d) \( 0.006932\ yr^{-1} \)
Show Answer & Explanation

Answer: (c) \( 0.06932\ yr^{-1} \)

Explanation:
1. \( \lambda=0.693/10=0.0693\ yr^{-1} \).

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 18: A radioactive isotope decays at such a rate that only 1/16 of the original amount remains after 192 minutes. The half-life of the isotope is
(a) 32 min
(b) 48 min
(c) 12 min
(d) 24 min
Show Answer & Explanation

Answer: (b) 48 min

Explanation:
1. 1/16 means 4 half-lives, so \( t_{1/2}=192/4=48 \) min.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 19: In the given reaction, \( {}^{235}_{92}\mathrm{U} \) \( \xrightarrow{-\alpha} \) A \( \xrightarrow{-\beta} \) B \( \xrightarrow{-\beta} \) C, the isotopes are
(a) A and C
(b) \( {}^{235}_{92}\mathrm{U} \) and C
(c) A and B
(d) A, B and C
Show Answer & Explanation

Answer: (b) \( {}^{235}_{92}\mathrm{U} \) and C

Explanation:
1. After alpha: Z = 90, A = 231 (A).
2. After beta: Z = 91 (B); after second beta: Z = 92, A = 231 (C).
3. U-235 and C both have Z = 92, so they are isotopes.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 20: For a radioactive decay with decay constant \( \lambda \), the average life is representative of
(a) \( 1/\lambda \)
(b) \( \ln2/\lambda \)
(c) \( \lambda/\sqrt2 \)
(d) \( 0.693/\lambda \)
Show Answer & Explanation

Answer: (a) \( 1/\lambda \)

Explanation:
1. Average life \( \tau=1/\lambda \), whereas \( 0.693/\lambda \) is the half-life.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 21: For a first order decay the rate constant is \( 2.34\ s^{-1} \). The half-life is
(a) 0.30 s
(b) 0.60 s
(c) 3.3 s
(d) data insufficient
Show Answer & Explanation

Answer: (a) 0.30 s

Explanation:
1. \( t_{1/2}=0.693/2.34=0.296\approx0.30\ s \).

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 22: The half-life of \( {}^{14}_{6}\mathrm{C} \) is 5770 years. The time after which 72% of the isotope is left is
(a) 2740 years
(b) 274 years
(c) 2780 years
(d) 278 years
Show Answer & Explanation

Answer: (a) 2740 years

Explanation:
1. \( t=\frac{2.303}{\lambda}\log\frac{100}{72}=\frac{5770\times2.303}{0.693}\times0.1427 \).
2. This is about 2740 years.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 23: A radioactive substance takes 20 min to decay 25%. How much time will be required to decay 75%?
(a) 96.4 min
(b) 68 min
(c) 964 min
(d) 680 min
Show Answer & Explanation

Answer: (a) 96.4 min

Explanation:
1. First order: \( k=\frac{2.303}{20}\log\frac{100}{75}=0.01438\ min^{-1} \).
2. For 75% decay: \( t=\frac{2.303}{k}\log4=96.4 \) min.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 24: A radioactive sample emits 64 times more radiation than the non-hazardous limit. If its half-life is 2 hours, after what time does it become non-hazardous?
(a) 16 hr
(b) 12 hr
(c) 8 hr
(d) 4 hr
Show Answer & Explanation

Answer: (b) 12 hr

Explanation:
1. 64 = \( 2^6 \), so 6 half-lives are needed.
2. Time = 6 \( \times \) 2 = 12 hours.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 25: The half-life of a radioactive element does not depend upon its amount. If 8.0 g of a radioactive isotope has a half-life of 10 hrs, the half-life of 2.0 g of the same substance is
(a) 2.5 hrs
(b) 5 hrs
(c) 10 hrs
(d) 40 hrs
Show Answer & Explanation

Answer: (c) 10 hrs

Explanation:
1. Half-life is independent of the quantity present, so it is still 10 hours.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

Question 26: A radioactive element has a half-life of 1 day. After three days the amount of the element left will be
(a) 1/2 of the original amount
(b) 1/4 of the original amount
(c) 1/8 of the original amount
(d) 1/16 of the original amount
Show Answer & Explanation

Answer: (c) 1/8 of the original amount

Explanation:
1. Three days = 3 half-lives, so \( (1/2)^3=1/8 \) remains.

Teacher's Note:
1. Identify the key concept in the question first, then apply the standard relation step by step.
2. Check units and the number of significant figures before choosing the option.

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