Name: Rutherford's Model of an Atom and Its Drawback
Uploaded: 2019-07-19
Duration: 5 min 50 s
Description: A scientist, Rutherford, in 1911, experimented with a gold foil and alpha particles to understand the structure of an atom. Explore the experiment and its ou...

Question

Give the order of magnitude of nuclear radius, nuclear mass density, and average atomic mass density Compare these densities with the typical mass densities of solids, liquids and gases at NTP.( mass of proton/neutron= $1.66 \times 10^{- 27} kg, R_{0} = 1.2 \times 10^{- 15} m$ )

Accepted Answer

The density of the nucleus is given by $ρ = \frac{3}{4} . \frac{m}{{πR}^{3}_{0}}$

Where $m$ = average mass of nucleon = $1.66 \times 10^{- 27} kg$

and $R_{0}$ , = empirical constant equal to $1.2 \times 10^{- 15} m$

Substituting these values in the above formula, we have

$ρ = \frac{3 \times 1.66 \times 10^{- 27}}{4 \times 3.14 \times {(1.2 \times 10^{- 15})}^{3}} = 2.29 \times 10^{17} kg / m^{3}$

This is $10^{13} - 10^{14}$ times the average atomic mass density, which is of the order of $10^{3} - 10^{4} {kgm}^{- 3}$

Typical mass densities of solids and liquids are of the same order as average atomic mass density since atoms are tightly packed in solids and liquids. Typical densities of gases at NTP are much smaller, of the order of $10^{- 1}$ to $1 kg m^{- 3}$ .and liquid (water)has density of $10^{3} kg / m^{3}$

Give the order of magnitude of nuclear radius, nuclear mass density, and average atomic mass density Compare these densities with the typical mass densities of solids, liquids and gases at NTP.( mass of proton/neutron= $1.66 \times 10^{- 27} kg, R_{0} = 1.2 \times 10^{- 15} m$ )

Important Questions on Nuclear Structure

Learn and Prepare for any exam you want !

Give the order of magnitude of nuclear radius, nuclear mass density, and average atomic mass density Compare these densities with the typical mass densities of solids, liquids and gases at NTP.( mass of proton/neutron=1.66×10-27kg, R0=1.2×10-15m)

Important Questions on Nuclear Structure

Learn and Prepare for any exam you want !

Give the order of magnitude of nuclear radius, nuclear mass density, and average atomic mass density Compare these densities with the typical mass densities of solids, liquids and gases at NTP.( mass of proton/neutron= $1.66 \times 10^{- 27} kg, R_{0} = 1.2 \times 10^{- 15} m$ )