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 Multiple Choice QuestionsMultiple Choice Questions

21.

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

  • 5: 4


D.

5: 4

Given 80 min = 4 half-lives of A = 2 half-lives of B.
Let the initial number of nuclei in each sample be N.

For radioactive element A,

NA after 80 min = N/24

⇒ Number of A nuclides decayed  =straight N minus straight N over 16 space equals space 15 over 16 straight N


For radioactive element B,

NB after 80 min  = N/22
⇒ Number of B nuclides decayed
straight N minus straight N over 4 space equals space 3 over 4 straight N
therefore, the ratio of decayed numbers of A and B nuclei will be

fraction numerator open parentheses 15 divided by 16 close parentheses straight N over denominator left parenthesis 3 divided by 4 right parenthesis straight N end fraction space equals space 5 over 4
385 Views

22.

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 4 over denominator straight Z minus 2 end fraction

B.

fraction numerator straight A minus straight Z minus 4 over denominator straight Z minus 4 end fraction

In positive beta decay a, proton is transformed into a neutron and a positron is emitted

p+ → n0 + e+
Number of neutrons initially was A-Z
Number of neutrons after decay (A-Z) -3 x 2  (due to alpha particles) + 2 x 1 (due to positive beta decay)
The number of protons will reduce by 8. so, the ratio number of neutrons to that of protons = fraction numerator straight A minus straight Z minus 4 over denominator straight Z minus 8 end fraction

549 Views

23.

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

  • 7 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
580 Views

24.

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


B.

 rα = rp< rd

For charged particle moving with a speed v, in magnetic field B, on a circular track of radius

straight r space equals space mv over qB space equals space fraction numerator square root of 2 km end root over denominator qB end fraction
open parentheses therefore space mv space equals space straight p space and space straight K space equals fraction numerator straight p squared over denominator 2 straight m end fraction space rightwards double arrow space straight p space equals space square root of 2 km end root close parentheses
rightwards double arrow space straight r space proportional to space fraction numerator square root of straight m over denominator straight q end fraction
or space straight m subscript straight d space equals 2 straight m subscript straight p space and space straight q subscript straight d space equals space straight q subscript straight p semicolon
straight m subscript straight alpha space equals space 4 straight m subscript straight p space and space straight q subscript straight alpha space equals space 2 straight q subscript straight p
rightwards double arrow straight r subscript straight p colon straight r subscript straight d colon straight r subscript straight alpha space equals space fraction numerator square root of straight m subscript straight p end root over denominator straight q subscript straight p end fraction colon fraction numerator square root of 2 straight m subscript straight p end root over denominator straight q subscript straight p end fraction colon fraction numerator square root of 4 straight m subscript straight p end root over denominator 2 straight q subscript straight p end fraction
space equals space 1 colon space square root of 2 colon 1
straight r subscript straight alpha space equals space straight r subscript straight p space less than thin space straight r subscript straight d

808 Views

25.

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

  • 5.4 MeV


A.

0.73 MeV

increment straight m space equals space left parenthesis straight m subscript straight p plus straight m subscript straight e right parenthesis minus straight m subscript straight n
space equals space 9 space straight x 10 to the power of negative 31 end exponent space kg.
Energy space released space equals space left parenthesis 9 space straight x space 10 to the power of negative 31 end exponent space kg right parenthesis space straight c squared space joules
space equals space fraction numerator 9 space straight x 10 to the power of negative 31 end exponent space straight x space left parenthesis 3 space straight x space 10 to the power of 8 right parenthesis squared over denominator 1.6 space straight x space 110 to the power of negative 13 end exponent end fraction space space MeV
space equals space 0.73 space MeV
1351 Views

26.

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 straight T space fraction numerator log space 1.3 over denominator log space 2 end fraction

D.

straight t space equals space straight T space fraction numerator log space 1.3 over denominator log space 2 end fraction

At time t
straight N subscript straight A space equals space fraction numerator straight N subscript 0 over denominator 1.3 end fraction

also let initially there are total N0 number of nuclei
NA + NB = N0
straight N subscript straight A space equals space fraction numerator straight N subscript 0 over denominator 1.3 end fraction
Also space as space we space know
straight N subscript straight A space space equals space straight N subscript 0 straight e to the power of negative λt end exponent
fraction numerator straight N subscript 0 over denominator 1.3 end fraction space equals space straight N subscript 0 straight e to the power of negative λt end exponent
fraction numerator 1 over denominator 1.3 end fraction space equals space straight e to the power of negative λt end exponent
rightwards double arrow space calligraphic l space n left parenthesis 1.3 right parenthesis space equals lambda t
t space equals space fraction numerator </div>		</div>
		<div class= 550 Views