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Nuclei · Question 31

AIPMT 2011 (Mains)MCQMedium📈 Topic in 25% papers+4−1
1

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0, the number of P species is 4N0 and that of Q is N0. Half-life of P (for conversion to R) is 1 minute whereas that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be

  1. 2N0
  2. 3N0
  3. 9N02
  4. 5N02

Answer

(3) 9N02

Solution

After time t (in minutes):

NP = 4N0 ( 12 )t/1 and NQ = N0 ( 12 )t/2

For NP = NQ: 4 ( 12 )t = ( 12 )t/2

2t/2 = 4 t = 4 min

NP = NQ = 4N016 = N04

Total nuclei are conserved: NR = 5N0 - ( N04 + N04 )

= 9N02

Answer: (3)

Out of syllabusAIPMT 2011 (Mains)

Keep practising — Nuclei

2

The power obtained in a reactor using 235U disintegration is 1000 kW. The mass decay of 235U per hour is

  1. 10 microgram
  2. 20 microgram
  3. 40 microgram
  4. 1 microgram
AIPMT 2011 (Prelims)
3

Fusion reaction takes place at high temperature because

  1. nuclei break up at high temperature
  2. atoms get ionised at high temperature
  3. kinetic energy is high enough to overcome the Coulomb repulsion between nuclei
  4. molecules break up at high temperature
AIPMT 2011 (Prelims)
4

The half life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was estimated to be

  1. 150 years
  2. 200 years
  3. 250 years
  4. 100 years
Out of syllabusAIPMT 2011 (Prelims)
5

A nucleus mnX emits one particle and two particles. The resulting nucleus is

  1. m-6n-4Z
  2. m-6nZ
  3. m-4nX
  4. m-4n-2Y
Out of syllabusAIPMT 2011 (Prelims)
6

The binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is

  1. 23.6 MeV
  2. 2.2 MeV
  3. 28.0 MeV
  4. 30.2 MeV
AIPMT 2010 (Mains)
7

The decay constant of a radioisotope is . If A1 and A2 are its activities at times t1 and t2 respectively, the number of nuclei which have decayed during the time (t1 - t2)

  1. A1t1 - A2t2
  2. A1 - A2
  3. (A1 - A2)/
  4. (A1 - A2)
Out of syllabusAIPMT 2010 (Mains)
8

The mass of a 73Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of 73Li nucleus is nearly

  1. 46 MeV
  2. 5.6 MeV
  3. 3.9 MeV
  4. 23 MeV
AIPMT 2010 (Prelims)
9

The activity of a radioactive sample is measured as N0 counts per minute at t = 0 and N0/e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is

  1. e 25
  2. 5 e 2
  3. 5 10 2
  4. 5 e 2
Out of syllabusAIPMT 2010 (Prelims)
10

In the nuclear decay given below AZX AZ+1Y A-4Z-1 B* A-4Z-1B, the particles emitted in the sequence are

  1. , ,
  2. , ,
  3. , ,
  4. , ,
Out of syllabusAIPMT 2009
11

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an

  1. isomer of parent
  2. isotone of parent
  3. isotope of parent
  4. isobar of parent
Out of syllabusAIPMT 2009

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