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Write the expression for distance of clo...

Write the expression for distance of closest approach for a `alpha`-particle.

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To derive the expression for the distance of closest approach for an alpha particle, we can follow these steps: ### Step 1: Understand the Concept The distance of closest approach refers to the minimum distance between the alpha particle and the nucleus when the alpha particle is approaching the nucleus. At this point, the kinetic energy of the alpha particle is converted into potential energy due to the electrostatic repulsion between the positively charged alpha particle and the positively charged nucleus. ### Step 2: Write the Kinetic Energy of the Alpha Particle The kinetic energy (KE) of the alpha particle can be expressed as: \[ ...
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Knowledge Check

  • Assertion (A) : The positively charged nucleus of an atom has a radius of almost 10^(-15) m. Reason (R) : In a-particle scattering experiment the distance of closest approach for alpha -particles is of the order of 10^(-15) m.

    A
    If both assertion and reason are true and the reason is the correct explanation of the assertion.
    B
    If both assertion and reason are true but reason is not the correct explanation of the assertion.
    C
    If assertion is true but reason is false.
    D
    If the assertion is false but reason is true.

  • Assertion: The positively changed nucleus of an atom has a radius of almost 10^(-15)m . Reason: In alpha -particle scattering experiment the distance of closest apporach for alpha -particles is ~~10^(-15)m .

    A
    If both assertion and reason are true and reason is the correct explanation of assertion.
    B
    If both assertion and reason are true but reason is not the correct explanation of assertion.
    C
    If assertion is true but reason is false.
    D
    If assertion is false but reason is true.

  • In scattering experiment, find the distance of closest approach, if a 6 MeV alpha - particle is used

    A
    `3.2 xx 10^(-16) m`
    B
    `2 xx 10^(-14) m`
    C
    `4.6 xx 10^(-15) m`
    D
    `3.2 xx 10^(-15)` m

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    Explore conceptually related problems

    Read the following passage and then answer questions (a) - (e) on the basis of your understanding of the passage and the related studied concepts. Rutherford was the pioneer who established the existence of the atomic nucleus. Result of Geiger and Marsden experiment on the scattering of a-particles from thin gold foils, performed at Rutherford’s suggestion, revealed that the distance of closest approach to a gold nucleus of an a-particle of kinetic energy 5.5 MeV is about 4.0 xx 10^(-14)m . The said scattering effect was explained by Rutherford by assuming that the Coulombian repulsive force was solely responsible for scattering. Since the positive charge is confined to the nucleus, the actual size of the nucleus has to be less than 4.0 xx 10^(-14) m. If we use a-particles of higher energies, the distance of closest approach to the gold nucleus will be still smaller. At some point the scattering will begin to be affected by the short range nuclear forces and differ from Rutherford’s calculations. From the distance at which deviations set it, nuclear size can be inferred. (a) Define MeV and express its value in terms of SI unit of energy. (b) What is distance of closest approach ? (c) Write an expression for distance of closest approach of a-particle to a gold nucleus. (d) What was Rutherford’s hypothesis regarding the existence of the atomic nucleus ? (e) How can you show that volume of the nucleus of an element is proportional to its mass number ?

    Define the distance of closest approach. An alpha -particle of kinetic enegy 'K' is bombarded on a thin gold foil. The distance of the closest approach is 'r' . What will be the distance of closest approach for an alpha -particle of double the kinetic energy ?

    Define distance of the closest approach. An alpha - particle of kinetic energy K is bombarded on a thin gold foil. The distance of the closest approach is r . What will be the distance of closest approach for an alpha -particle of double the kinetic energy ?

    Define distance of closest approach and impact parameter.

    In mu-particle scattering experiment, the expression of distance of closest approach ( r_0 )is (symbols have their usual meanings)

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