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Answer the following.
Assuming that nuclei are spherical in shape, whose radius R is given by where is a constant, show…
(a)[1.6666666666666667]
Assuming that nuclei are spherical in shape, whose radius R is given by $R = R_0 A^{1/3}$ where $R_0$ is a constant, show that the nuclear density (i.e. density of nuclear matter) is independent of mass number (A) of the nucleus / atom.
(b)[1.6666666666666667]
What are isotones?
(c)[1.6666666666666667]
Name the series of lines in hydrogen spectrum which lies in:
(1) Visible region
(2) UV region
Answer
Answer (a)
AIProof that nuclear density is independent of mass number:
$R = R_0 A^{1/3}$
Volume $V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi R_0^3 A$
Mass of nucleus $M = mA$ (where $m$ is average nucleon mass)
Nuclear density $\rho = \frac{M}{V} = \frac{mA}{\frac{4}{3}\pi R_0^3 A} = \frac{3m}{4\pi R_0^3}$
As $A$ cancels out, nuclear matter density is independent of mass number $A$.
- Radius of nucleus $R = R_0 A^{1/3}$, where $R_0$ is a constant and $A$ is mass number.
- Volume of spherical nucleus $V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi (R_0 A^{1/3})^3 = \frac{4}{3}\pi R_0^3 A$.
- Mass of nucleus $M = m A$, where $m$ is average mass of a nucleon.
- Nuclear density $\rho = \frac{M}{V} = \frac{mA}{\frac{4}{3}\pi R_0^3 A} = \frac{3m}{4\pi R_0^3}$.
- Since $m$ and $R_0$ are constants and $A$ cancels out, the nuclear density $\rho$ is independent of mass number $A$.
Answer (b)
AIIsotones are nuclides/atoms of different elements having the same number of neutrons ($N = A - Z$) but different mass numbers ($A$) and atomic numbers ($Z$).
Answer (c)
AI(1) Visible region: Balmer series.
(2) UV region: Lyman series.
From ISC 2027 Specimen Physics Paper 1, question 19(ii).