Advertisements
Advertisements
प्रश्न
Answer the following question.
Show that the density of the nucleus is independent of its mass number A.
Show that nuclear density in a given nucleus is independent of mass number A.
Advertisements
उत्तर १
Density of the nucleus = `(\text { mass of nucleus})/(\text { volume of nucleus})`
Mass of the nucleus = A amu = A × 1.66 × 10-27 kg
Volume of the nucleus = `4/3πR^3 = 4/3π(R_0A^(1/3))^3 A =4/3πR_0^3 A`
Thus, density = `(Axx1.66 xx10^(-27))/((4/3πR_0^3)A)` = `(1.66 xx 10^-27)/((4/3πR_0^3)`
which shows that the density is independent of mass number A.
Using R0 = 1.1 × 10-15 m and density = 2.97 × 1017 kg m-3
उत्तर २
Density = `("p") = "m"/"v"`
R = `"R"_0("A")^(1/3)`
Volume = `(4)/(3)"πR"^3`
Volume of atom = `(4)/(3)π ("R"_0 "A"^(1/3))^3`
= `(4)/(3)π"R"_0^3"A"`
Density = `"mass"/"volume"`
`"p" = ("m"."A")/((4)/(3) "πR"_0^3 "A")`
`"p" = ("m")/((4)/(3) "πR"_0^3)`
m = mass of proton
It shows independence in mass.
APPEARS IN
संबंधित प्रश्न
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 mass number of He is 4 and that for sulphur is 32. The radius of sulphur nuclei is larger than that of helium by:
How is the nuclear radius defined?
Which relation gives the experimentally observed dependence of the nuclear radius \[R\] on the mass number \[A\]?
The minimum distance reached by an alpha particle approaching a positively charged nucleus before being turned back is called the:
If the mass number \[A\] of a nucleus increases, its radius increases as \[A^{1/3}\]. This implies that:
Since the nucleus is approximately spherical with \[R = R_0 A^{1/3}\], its volume \[V = \frac{4}{3}\pi R^3\] is proportional to:
The approximate density of nuclear matter is:
The density of matter in a neutron star is:
