The half life of a radioactive substance is 20 minutes. The appr

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be:

  • 1: 16

  • 4 : 1

  • 1: 4

  • 1: 4

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2.

Proton, Deuteron and alpha particle of the same kinetic energy is moving in circular trajectories in a constant magnetic field. The radii of the proton, deuteron and alpha particle are respectively rp, rd and rα. Which one of the following relations is correct?

  •  rα = rp= rd

  •  rα = rp< rd

  •  rα > rd> rp

  •  rα > rd> rp

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3.

Assume that a neutron breaks into a proton and an electron. The energy released during this process is(Mass of neutron = 1.6725 x 10–27kg; mass of proton = 1.6725 x 10–27kg; mass of electron = 9 x 10–31kg)

  • 0.73 MeV

  • 7.10 MeV

  • 6.30 MeV

  • 6.30 MeV

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4.

The half life of a radioactive substance is 20 minutes. The approximate time interval (t2 - t1) between the time t2 when 2/3 of it has decayed and time t1 when 1/3 of it had decayed is

  • 14 min

  • 20 min

  • 28 min

  • 28 min


B.

20 min

2 over 3 straight N subscript 0 space equals space straight N subscript 0 straight e to the power of negative λt subscript 1 end exponent
1 third straight N subscript 0 space equals space straight N subscript 0 straight e to the power of negative λt subscript 2 end exponent
2 space equals straight e to the power of straight lambda left parenthesis space straight t subscript 2 minus straight t subscript 1 right parenthesis end exponent
straight lambda left parenthesis straight t subscript 2 minus straight t subscript 1 right parenthesis space equals space l n 2
left parenthesis straight t subscript 2 minus straight t subscript 1 right parenthesis space equals space fraction numerator l straight n begin display style 2 end style over denominator straight lambda end fraction space equals space 20 space min
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5.

A nucleus of mass M + Δm is at rest and decays into two daughter nuclei of equal mass M/2 each. The speed of light is c.
The binding energy per nucleon for the parent nucleus is E1 and that for the daughter nuclei is E2. Then

  • E1 = 2E2

  • E2 = 2E1

  • E1 > E2

  • E1 > E2

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6.

A nucleus of mass M + Δm is at rest and decays into two daughter nuclei of equal mass M/2 each. Speed of light is c.

The speed of daughter nuclei is

  • fraction numerator increment straight m over denominator straight M plus increment straight m end fraction
  • square root of fraction numerator 2 increment straight m over denominator straight M end fraction end root
  • straight c square root of fraction numerator increment straight m over denominator straight M end fraction end root
  • straight c square root of fraction numerator increment straight m over denominator straight M end fraction end root
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7.

A radioactive nucleus (initial mass number A and atomic number Z) emits 3 α–particles and 2 positions. The ratio of number of neutrons to that of protons in the final nucleus will be

  • fraction numerator straight A minus straight Z minus 8 over denominator straight Z minus 4 end fraction
  • fraction numerator straight A minus straight Z minus 4 over denominator straight Z minus 4 end fraction
  • fraction numerator straight A minus straight Z minus 12 over denominator straight Z minus 4 end fraction
  • fraction numerator straight A minus straight Z minus 12 over denominator straight Z minus 4 end fraction
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8.

A radioactive nucleus A with a half-life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by

  • t = T log (1.3)

  • straight t space equals space fraction numerator straight T over denominator log space left parenthesis 1.3 right parenthesis end fraction
  • straight t space equals space fraction numerator straight T space log space 2 over denominator 2 space log space 1.3 end fraction
  • straight t space equals space fraction numerator straight T space log space 2 over denominator 2 space log space 1.3 end fraction
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9.

The above is a plot of binding energy per nucleon Eb, against the nuclear mass M; A, B, C, D, E, F correspond to different nuclei. Consider four reactions:

(i) A + B → C + ε  (ii) C → A + B + ε
(iii) D + E → F + ε and (iv) F → D + E +ε

where ε is the energy released? In which reaction is ε positive?

  • (i) and (iv)

  • (i) and (iii)

  • (ii) and (iv)

  • (ii) and (iv)

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10.

The transition from the state n = 4 to n = 3 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

  • 2 → 1

  • 3 → 2

  • 4 → 2

  • 4 → 2

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