If the nuclear radius of \(^{27}\text{Al}\) is \(3.6\) Fermi, the approximate nuclear radius of \(^{64}\text{Cu}\) in Fermi is:
1. \(2.4\)
2. \(1.2\)
3. \(4.8\)
4. \(3.6\)
If \(M(A,~Z)\), \(M_p\), and \(M_n\) denote the masses of the nucleus \(^{A}_{Z}X,\) proton, and neutron respectively in units of \(u\) (\(1~u=931.5~\text{MeV/c}^2\)) and represent its binding energy \((BE)\) in \(\text{MeV}\). Then:
1. | \(M(A, Z) = ZM_p + (A-Z)M_n- \frac{BE}{c^2}\) |
2. | \(M(A, Z) = ZM_p + (A-Z)M_n+ BE\) |
3. | \(M(A, Z) = ZM_p + (A-Z)M_n- BE\) |
4. | \(M(A, Z) = ZM_p + (A-Z)M_n+ \frac{BE}{c^2}\) |
Two nuclei have their mass numbers in the ratio of \(1:3.\) The ratio of their nuclear densities would be:
1. \(1:3\)
2. \(3:1\)
3. \((3)^{1/3}:1\)
4. \(1:1\)
In the radioactive decay process, the negatively charged emitted β-particles are:
1. | the electrons present inside the nucleus |
2. | the electrons produced as a result of the decay of neutrons inside the nucleus |
3. | the electrons produced as a result of collisions between atoms |
4. | the electrons orbiting around the nucleus |
If the radius of \(_{13}^{27}\mathrm{Al}\) nucleus is taken to be \(\mathrm{R}_{\mathrm{Al}},\) then the radius of \(_{53}^{125}\mathrm{Te}\) nucleus is near:
1. \(\left(\frac{53}{13}\right) ^{\frac{1}{3}}~\mathrm{R_{Al}}\)
2. \(\frac{5}{3}~\mathrm{R_{Al}}\)
3. \(\frac{3}{5}~\mathrm{R_{Al}}\)
4. \(\left(\frac{13}{53}\right)~\mathrm{R_{Al}}\)
For radioactive material, the half-life is \(10\) minutes. If initially, there are \(600\) number of nuclei, the time taken (in minutes) for the disintegration of \(450\) nuclei is :
1. \(20\)
2. \(10\)
3. \(30\)
4. \(15\)
Binding energy per nucleon plot against the mass number for stable nuclei is shown in the figure. Which curve is correct ?
1. A
2. B
3. C
4. D
The dependence of binding energy per nucleon, on the mass number, A, is represented by