The unit of length convenient on the nuclear scale is a fermi: $1 \mathrm{f}={10}^{-15} \mathrm{m}$. Nuclear sizes obey roughly the following empirical relation: $r=r_0\mathit{ }{A}^{1/3}$ where $r$ is the radius of the nucleus, $A$ its mass number, and $r_0$ is a constant equal to $1.2 \mathrm{f}$. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom i.e $0.58\times {10}^3 {\mathrm{kgm}}^{-3}$.

Measurement of any physical quantity is expressed in terms of an internationally accepted certain basic standard called unit.

2. Fundamental Units:

3. Supplementary Units:

4. Metric Prefixes:

5. Errors in measurements:

(i) Values obtained from several measurements are a1,a2, a3…. an: Mean value $a_{mean}= \frac{a_1+a_2+\dots a_n}{n}$

(ii) Absolute error of a measurement $\mathrm{\Delta }{a}_1= a_1-a_{mean}$

(iii) Mean absolute error $\mathrm{\Delta }{a}_{mean}= \frac{\mathrm{\Delta }{a}_1+\mathrm{\Delta }{a}_2+.\dots ..\mathrm{\Delta }{a}_n.}{n}$

(iv) Any measurement we take for the physical quantity a may lie between amean+Δamean and amean-Δamean

(v) Relative error in $= \frac{\mathrm{\Delta }{a}_{mean}}{a_{mean}}$

(vi) Percentage error $= \frac{\mathrm{\Delta }{a}_{mean}}{a_{mean}}\times 100\%$

6. Combination of errors:

(i) If two physical quantities A and B have measured values a±Δa and b±Δb and if $Z= A+B$ and $Z$ is expressed as z±Δz, then $z= a+b$ and $\mathrm{\Delta }z= \mathrm{\Delta }a+\mathrm{\Delta }b$

(ii) If $Z= A-B$ and Z is expressed as z±Δz, then $z= a-b$ and $\mathrm{\Delta }z= \mathrm{\Delta }a+\mathrm{\Delta }b$

(iii) If $Z= A\times B$ and Z is expressed as z±Δz, then $z= a\times b$ and $\mathrm{\Delta }z= z\left(\frac{\mathrm{\Delta }a}{a}+\frac{\mathrm{\Delta }b}{b}\right)$

(iv) If $Z= A÷B$ and Z is expressed as z±Δz, then $z= a÷b$ and $\mathrm{\Delta }z= z\left(\frac{\mathrm{\Delta }a}{a}+\frac{\mathrm{\Delta }b}{b}\right)$

(v) If $Z= A^n$ and Z is expressed as z±Δz, then $z= a^n$ and $\mathrm{\Delta }z= n\left(z\left(\frac{\mathrm{\Delta }a}{a}\right)\right)$