Question

(a) An aspiring physicist wants to build a scale model of a hydrogen atom for her science fair project. If the atom is 1.00 m diameter, how big should she try to make the nucleus?

(b) How easy will this be to do?

Short answer

(a) The size of the nucleus on the scale model of hydrogen atom with 1.00 mdiameter should be 10 μm.

(b) It will not be hard to build a scale model of a hydrogen atom of approximately the calculated size.

Step-by-step solution

Determine the formulas:

Consider the formulas for the diameter ratios is:

\(\frac{{{{\bf{d}}_{\bf{N}}}}}{{{{\bf{d}}_{\bf{\alpha }}}}}{\bf{ = }}\frac{{{{\bf{D}}_{\bf{N}}}}}{{{{\bf{D}}_{\bf{\Lambda }}}}}\)

Here,d_N the diameter of nucleus, d_a diameter of actual atom, D_Nis the diameter of the nucleus on the scale model, and D_A is the diameter of the atom on the scale model.

Find the size of the nucleus on the scale model of hydrogen atom

(a)

Substitute the values and solve for the size of the nucleus as follows:

\(\begin{array}{l}\frac{{\left( {{{10}^{ - 15}}\;{\rm{m}}} \right)}}{{\left( {{{10}^{ - 10}}\;{\rm{m}}} \right)}} = \frac{{{D_N}}}{{1\;{\rm{m}}}}\\{D_N} = \frac{{\left( {{{10}^{ - 15}}\;{\rm{m}}} \right)\left( {1\;{\rm{m}}} \right)}}{{\left( {{{10}^{ - 10}}\;{\rm{m}}} \right)}}\\{D_N} = 10\;{\rm{\mu m}}\end{array}\)

Therefore, the required size of the nucleus on the scale model of hydrogen atom with with 1.00 mdiameter should be 10 μm.

Find how this will be easy to do

(b)

Consider the size of the nucleus must be 10 μm so that the scale model of the hydrogen atom can be build that have the diameter of 1.00 m. The stated size model is not difficult to make but the scale size model of 10 μm will be complex.

Therefore, it will not be hard to build a scale model of a hydrogen atom of approximately the calculated size.