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Question
The ratio of the nuclear densities of two nuclei having mass numbers 64 and 125 is ______.
Options
`64/125`
`4/5`
`5/4`
1
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Solution
The ratio of the nuclear densities of two nuclei having mass numbers 64 and 125 is 1.
Explanation:
Given, A1 = 64, A2 = 125
`R = R_0A^{1"/"3}`
Density = `"Atomic Mass"/"Volume" = A/(4/3piR^3)`
= `A/(4/3piR^3) = A/(4/3pi(R_0A^{1"/"3})^3)`
= `A/(4/3piR_0^3A)`
`rho = 1/(4/3piR_0^3)`
`rho_1/rho_2 = (4/3piR_0^3)/(4/3piR_0^3) = 1`
It is independent of mass number.
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