363861
The radius of \(_{29}C{u^{64}}\) nucleus in Fermi is (given \({R_0} = 1.2 \times {10^{ - 15}}m\))
1 \(4.8\)
2 \(1.2\)
3 \(7.7\)
4 \(9.6\)
Explanation:
Nuclear radius \(R = {R_0}{A^{1/3}}\) Where \({R_0}\left( { = 1.2 \times {{10}^{ - 15}}m} \right)\) is a constant and \(A\) is the mass number \({R_{Cu}} = \left( {1.2 \times {{10}^{ - 15}}m} \right){\left( {64} \right)^{1/3}}\) \( = \left( {1.2 \times {{10}^{ - 15}}m} \right){\left( {{4^3}} \right)^{1/3}}\) \( = 4.8 \times {10^{ - 15}}m = 4.8fm\)\(\left( {\because 1fm = {{10}^{ - 15}}m = 1\,{\text{Fermi}}} \right)\)
KCET - 2012
PHXII13:NUCLEI
363862
The density of a nucleus in which mass of each nucleon is \(1.67 \times {10^{27}}\;kg\) and is \({R_0} = 1.4 \times {10^{ - 15}}\;m.\)
1 \(1.453 \times {10^{17}}\;kg{\rm{/}}{m^3}\)
2 \(1.453 \times {10^{16}}\;kg{\rm{/}}{m^3}\)
3 \(1.453 \times {10^{21}}\;kg{\rm{/}}{m^3}\)
4 \(1.453 \times {10^{10}}\;kg{\rm{/}}{m^3}\)
Explanation:
\(d = \frac{{Am}}{{\frac{4}{3}\pi {R^3}}} = \frac{{3{\rm{Am}}}}{{4\pi \left( {{R_0}{A^{\frac{1}{3}}}} \right)}}\) \( = \frac{{3{\rm{Am}}}}{{4\pi R_0^3A}} = \frac{{3m}}{{4\pi R_0^3}}.\) Where \({R_0} = 1.4 \times {10^{ - 15}}\;m\) and \(m\) is the mass of nucleon which is \(1.67 \times {10^{27}}\;kg\) \( = d = 1.453 \times {10^{17}}\;kg{\rm{/}}{m^3}\)
PHXII13:NUCLEI
363863
The graph of ln \((R/{R_0})\) versus ln \(A\) (\(R = \) radius) of nucleus (\(A\) is atomic number).
1 Straight line
2 Parabola
3 Ellipse
4 Circle
Explanation:
\(R = {R_0}{A^{1/3}}\) \(\frac{R}{{{R_0}}} = {A^{1/3}} \Rightarrow \ln \frac{R}{{{R_0}}} = \frac{1}{3}\ln A\) The graph between \(\ln \left( {\frac{R}{{{R_0}}}} \right)\) and \(\ln A\) is a straight line.
PHXII13:NUCLEI
363864
A nucleus \(x^{235}\) splits into two nuclei having the mass numbers in the ratio \(2: 1\). The ratio of the radii of those two nuclei is
363861
The radius of \(_{29}C{u^{64}}\) nucleus in Fermi is (given \({R_0} = 1.2 \times {10^{ - 15}}m\))
1 \(4.8\)
2 \(1.2\)
3 \(7.7\)
4 \(9.6\)
Explanation:
Nuclear radius \(R = {R_0}{A^{1/3}}\) Where \({R_0}\left( { = 1.2 \times {{10}^{ - 15}}m} \right)\) is a constant and \(A\) is the mass number \({R_{Cu}} = \left( {1.2 \times {{10}^{ - 15}}m} \right){\left( {64} \right)^{1/3}}\) \( = \left( {1.2 \times {{10}^{ - 15}}m} \right){\left( {{4^3}} \right)^{1/3}}\) \( = 4.8 \times {10^{ - 15}}m = 4.8fm\)\(\left( {\because 1fm = {{10}^{ - 15}}m = 1\,{\text{Fermi}}} \right)\)
KCET - 2012
PHXII13:NUCLEI
363862
The density of a nucleus in which mass of each nucleon is \(1.67 \times {10^{27}}\;kg\) and is \({R_0} = 1.4 \times {10^{ - 15}}\;m.\)
1 \(1.453 \times {10^{17}}\;kg{\rm{/}}{m^3}\)
2 \(1.453 \times {10^{16}}\;kg{\rm{/}}{m^3}\)
3 \(1.453 \times {10^{21}}\;kg{\rm{/}}{m^3}\)
4 \(1.453 \times {10^{10}}\;kg{\rm{/}}{m^3}\)
Explanation:
\(d = \frac{{Am}}{{\frac{4}{3}\pi {R^3}}} = \frac{{3{\rm{Am}}}}{{4\pi \left( {{R_0}{A^{\frac{1}{3}}}} \right)}}\) \( = \frac{{3{\rm{Am}}}}{{4\pi R_0^3A}} = \frac{{3m}}{{4\pi R_0^3}}.\) Where \({R_0} = 1.4 \times {10^{ - 15}}\;m\) and \(m\) is the mass of nucleon which is \(1.67 \times {10^{27}}\;kg\) \( = d = 1.453 \times {10^{17}}\;kg{\rm{/}}{m^3}\)
PHXII13:NUCLEI
363863
The graph of ln \((R/{R_0})\) versus ln \(A\) (\(R = \) radius) of nucleus (\(A\) is atomic number).
1 Straight line
2 Parabola
3 Ellipse
4 Circle
Explanation:
\(R = {R_0}{A^{1/3}}\) \(\frac{R}{{{R_0}}} = {A^{1/3}} \Rightarrow \ln \frac{R}{{{R_0}}} = \frac{1}{3}\ln A\) The graph between \(\ln \left( {\frac{R}{{{R_0}}}} \right)\) and \(\ln A\) is a straight line.
PHXII13:NUCLEI
363864
A nucleus \(x^{235}\) splits into two nuclei having the mass numbers in the ratio \(2: 1\). The ratio of the radii of those two nuclei is
363861
The radius of \(_{29}C{u^{64}}\) nucleus in Fermi is (given \({R_0} = 1.2 \times {10^{ - 15}}m\))
1 \(4.8\)
2 \(1.2\)
3 \(7.7\)
4 \(9.6\)
Explanation:
Nuclear radius \(R = {R_0}{A^{1/3}}\) Where \({R_0}\left( { = 1.2 \times {{10}^{ - 15}}m} \right)\) is a constant and \(A\) is the mass number \({R_{Cu}} = \left( {1.2 \times {{10}^{ - 15}}m} \right){\left( {64} \right)^{1/3}}\) \( = \left( {1.2 \times {{10}^{ - 15}}m} \right){\left( {{4^3}} \right)^{1/3}}\) \( = 4.8 \times {10^{ - 15}}m = 4.8fm\)\(\left( {\because 1fm = {{10}^{ - 15}}m = 1\,{\text{Fermi}}} \right)\)
KCET - 2012
PHXII13:NUCLEI
363862
The density of a nucleus in which mass of each nucleon is \(1.67 \times {10^{27}}\;kg\) and is \({R_0} = 1.4 \times {10^{ - 15}}\;m.\)
1 \(1.453 \times {10^{17}}\;kg{\rm{/}}{m^3}\)
2 \(1.453 \times {10^{16}}\;kg{\rm{/}}{m^3}\)
3 \(1.453 \times {10^{21}}\;kg{\rm{/}}{m^3}\)
4 \(1.453 \times {10^{10}}\;kg{\rm{/}}{m^3}\)
Explanation:
\(d = \frac{{Am}}{{\frac{4}{3}\pi {R^3}}} = \frac{{3{\rm{Am}}}}{{4\pi \left( {{R_0}{A^{\frac{1}{3}}}} \right)}}\) \( = \frac{{3{\rm{Am}}}}{{4\pi R_0^3A}} = \frac{{3m}}{{4\pi R_0^3}}.\) Where \({R_0} = 1.4 \times {10^{ - 15}}\;m\) and \(m\) is the mass of nucleon which is \(1.67 \times {10^{27}}\;kg\) \( = d = 1.453 \times {10^{17}}\;kg{\rm{/}}{m^3}\)
PHXII13:NUCLEI
363863
The graph of ln \((R/{R_0})\) versus ln \(A\) (\(R = \) radius) of nucleus (\(A\) is atomic number).
1 Straight line
2 Parabola
3 Ellipse
4 Circle
Explanation:
\(R = {R_0}{A^{1/3}}\) \(\frac{R}{{{R_0}}} = {A^{1/3}} \Rightarrow \ln \frac{R}{{{R_0}}} = \frac{1}{3}\ln A\) The graph between \(\ln \left( {\frac{R}{{{R_0}}}} \right)\) and \(\ln A\) is a straight line.
PHXII13:NUCLEI
363864
A nucleus \(x^{235}\) splits into two nuclei having the mass numbers in the ratio \(2: 1\). The ratio of the radii of those two nuclei is
363861
The radius of \(_{29}C{u^{64}}\) nucleus in Fermi is (given \({R_0} = 1.2 \times {10^{ - 15}}m\))
1 \(4.8\)
2 \(1.2\)
3 \(7.7\)
4 \(9.6\)
Explanation:
Nuclear radius \(R = {R_0}{A^{1/3}}\) Where \({R_0}\left( { = 1.2 \times {{10}^{ - 15}}m} \right)\) is a constant and \(A\) is the mass number \({R_{Cu}} = \left( {1.2 \times {{10}^{ - 15}}m} \right){\left( {64} \right)^{1/3}}\) \( = \left( {1.2 \times {{10}^{ - 15}}m} \right){\left( {{4^3}} \right)^{1/3}}\) \( = 4.8 \times {10^{ - 15}}m = 4.8fm\)\(\left( {\because 1fm = {{10}^{ - 15}}m = 1\,{\text{Fermi}}} \right)\)
KCET - 2012
PHXII13:NUCLEI
363862
The density of a nucleus in which mass of each nucleon is \(1.67 \times {10^{27}}\;kg\) and is \({R_0} = 1.4 \times {10^{ - 15}}\;m.\)
1 \(1.453 \times {10^{17}}\;kg{\rm{/}}{m^3}\)
2 \(1.453 \times {10^{16}}\;kg{\rm{/}}{m^3}\)
3 \(1.453 \times {10^{21}}\;kg{\rm{/}}{m^3}\)
4 \(1.453 \times {10^{10}}\;kg{\rm{/}}{m^3}\)
Explanation:
\(d = \frac{{Am}}{{\frac{4}{3}\pi {R^3}}} = \frac{{3{\rm{Am}}}}{{4\pi \left( {{R_0}{A^{\frac{1}{3}}}} \right)}}\) \( = \frac{{3{\rm{Am}}}}{{4\pi R_0^3A}} = \frac{{3m}}{{4\pi R_0^3}}.\) Where \({R_0} = 1.4 \times {10^{ - 15}}\;m\) and \(m\) is the mass of nucleon which is \(1.67 \times {10^{27}}\;kg\) \( = d = 1.453 \times {10^{17}}\;kg{\rm{/}}{m^3}\)
PHXII13:NUCLEI
363863
The graph of ln \((R/{R_0})\) versus ln \(A\) (\(R = \) radius) of nucleus (\(A\) is atomic number).
1 Straight line
2 Parabola
3 Ellipse
4 Circle
Explanation:
\(R = {R_0}{A^{1/3}}\) \(\frac{R}{{{R_0}}} = {A^{1/3}} \Rightarrow \ln \frac{R}{{{R_0}}} = \frac{1}{3}\ln A\) The graph between \(\ln \left( {\frac{R}{{{R_0}}}} \right)\) and \(\ln A\) is a straight line.
PHXII13:NUCLEI
363864
A nucleus \(x^{235}\) splits into two nuclei having the mass numbers in the ratio \(2: 1\). The ratio of the radii of those two nuclei is
