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Question

The ratio of the radii of the hydrogen atom and its nucleus is~105. Assuming the atom and the nucleus to be spherical,

(i) What will be the ratio of their sizes?

(ii) If the atom is represented by planet earth Re=6.4×106m, estimate the size of the nucleus.


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Solution

(i)

Step 1: Volume of a sphere

  • The volume of a sphere is given by V=34πr3
  • Let "R" be the radius of the atom and "r"be that of the nucleus.
  • For the radii of the hydrogen atom and its nucleus, its volume is

VH=34πrH31Vn=34πrn32

Step 2: Volume of the atom and its nucleus:

  • The ratio of the radii of the hydrogen atom and its nucleus is ~105
    rHrn=105

Step 3: Ratio of their volumes:

  • The ratio of their volumes,

VHVn=43πrH343πrn3VHVn=rH3rn3(rHrn=105)VHVn=(105)3
(ii)

Step 1: Ratio of the radius of earth and nucleus:

  • If the atom is represented by the planet Earth, Re=6.4×106m then the radius of the nucleus would be given by rn

Re=6.4×106m

  • We know that the ratio of the radius of the earth and the radius of the nucleus,

ReRn=105

Step 2: Radius of the nucleus:

ReRn=1056.4x106105=RnRn=6.4x10Rn=64m


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