Advertisements
Advertisements
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
Advertisements
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.
APPEARS IN
RELATED QUESTIONS
From the relation R = R0A1/3, where R0 is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).
Answer the following question.
Show that the density of the nucleus is independent of its mass number A.
A molecule of hydrogen contains two protons and two electrons. The nuclear force between these two protons is always neglected while discussing the behaviour of a hydrogen molecule. Why?
The radius of inner most orbit of hydrogen atom is 5.3 × 10-11 m. What is the radius of third allowed orbit of hydrogen atom?
The stable nucleus that has a radius half that of Fe56 is:
Calculate approximately the ratio of the nuclear radii of the gold isotope \[_{79}^{197}Au\] and the silver isotope \[_{47}^{107}Ag\].
The mass number of He is 4 and that for sulphur is 32. The radius of sulphur nuclei is larger than that of helium by:
The Q value of a nuclear reaction A + b → C + d is defined by Q = [mA + mb − mC − md]c² where the masses refer to the respective nuclei. Calculate the Q-value of the reaction and state whether this reaction is exothermic or endothermic.
\[_1^1\mathrm{H}+_1^3\mathrm{H}\rightarrow_1^2\mathrm{H}+_1^2\mathrm{H}\]
Atomic masses are given to be
\[\mathrm{m(}_{1}^{1}\mathrm{H)}=1.007825\mathrm{u}\]
\[\mathrm{m(}_{1}^{2}\mathrm{H)}=2.014102\mathrm{u}\]
\[\mathrm{m(}_{1}^{3}\mathrm{H})=3.016049\mathrm{u}\]
Assertion (A): All nuclei are not of the same size.
Reason (R): The size of the nucleus depends on atomic mass.
A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to 2:1. What will be the ratio of their nuclear size (nuclear radius)?
