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Nuclei

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Question 1
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A nuclear transformation is denoted by X(n, α) Li presubscript 3 presuperscript 7. Which of the following is the nucleus of element X?

  • straight C presuperscript 12 subscript 6
  • straight B presubscript 5 presuperscript 10
  • straight B presubscript 5 presuperscript 9
  • Be presubscript 4 presuperscript 11

Solution

B.

straight B presubscript 5 presuperscript 10 straight X space plus space straight n presubscript 0 presuperscript 1 space rightwards arrow with space space on top space He presubscript 2 presuperscript 4 space plus space Li presubscript 3 presuperscript 7
Question 2
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A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2:1. The ratio of their nuclear sizes will be

  • 21/3:1

  • 1:31/2

  • 31/2:1

  • 1:21/3

Solution

B.

1:31/2

Law of conservation of momentum gives
m1 v1 = m2 v2
straight m subscript 1 over straight m subscript 2 space equals straight v subscript 2 over straight v subscript 1 space But space space straight m space equals space 4 over 3 πr cubed straight rho or space straight m proportional to space straight r cubed therefore space straight m subscript 1 over straight m subscript 2 space equals space fraction numerator straight r subscript 1 superscript 3 over denominator straight r subscript 2 superscript 3 end fraction space equals space straight v subscript 2 over straight v subscript 1 straight r subscript 1 over straight r subscript 2 space equals space open parentheses 1 half close parentheses to the power of 1 divided by 3 end exponent straight r subscript 1 space colon straight r subscript 2 space equals space 1 space colon 2 to the power of 1 divided by 3 end exponent

Question 3
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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 space square root of fraction numerator increment straight m over denominator straight M space plus space increment straight m end fraction end root

Solution

B.

square root of fraction numerator 2 increment straight m over denominator straight M end fraction end root

Conserving the momentum
0 space equals space space straight M over 2 straight V subscript 1 space minus space straight M over 2 space straight V subscript 2 space left parenthesis therefore space initial space Velocity space equals space 0 right parenthesis rightwards double arrow space straight v subscript 1 space equals space straight v subscript 2 space..... space left parenthesis straight i right parenthesis
Now, from energy conservation and mass -energy equivalence

Question 4
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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

  • E2 > E1

Solution

D.

E2 > E1

After decay, the daughter nuclei will be more stable hence, binding energy per nucleon will be more than that of their parent nucleus.

Question 5
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A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 1 /2 m away, the number of electrons emitted by photocathode would

  • decrease by a factor of 4

  • increase by a factor of 4

  • decrease by a factor of 2

  • increase by a factor of 2

Solution

B.

increase by a factor of 4

On doubling the distance the intensity becomes one fourth i.e. only one-fourth of photons now strike the target in comparison to the previous number. Since the photoelectric effect is a one photon-one electron phenomenon, so only one-fourth photoelectrons are emitted out of the target hence reducing the current to one fourth the previous value.

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