The mass of a nucleus $$_Z^AX$$ is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table below :
| $$_1^1H$$ | 1.007825 u | $$_1^2H$$ | 2.014102 u |
|---|---|---|---|
| $$_3^6Li$$ | 6.015123 u | $$_3^7Li$$ | 7.016004 u |
| $$_{64}^{152}Gd$$ | 151.919803 u | $$_{82}^{206}Pb$$ | 205.974455 u |
| $$_1^3H$$ | 3.016050 u | $$_2^4He$$ | 4.002603 u |
| $$_{30}^{70}Zn$$ | 69.925325 u | $$_{34}^{82}Se$$ | 81.916709 u |
| $$_{83}^{209}Bi$$ | 208.980388 u | $$_{84}^{210}Po$$ | 209.982876 u |
(1 u = 932 MeV/c2)
The correct statement is
The mass of a nucleus $$_Z^AX$$ is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m3 + m4) > M'. The masses of some neutral atoms are given in the table below :
| $$_1^1H$$ | 1.007825 u | $$_1^2H$$ | 2.014102 u |
|---|---|---|---|
| $$_3^6Li$$ | 6.015123 u | $$_3^7Li$$ | 7.016004 u |
| $$_{64}^{152}Gd$$ | 151.919803 u | $$_{82}^{206}Pb$$ | 205.974455 u |
| $$_1^3H$$ | 3.016050 u | $$_2^4He$$ | 4.002603 u |
| $$_{30}^{70}Zn$$ | 69.925325 u | $$_{34}^{82}Se$$ | 81.916709 u |
| $$_{83}^{209}Bi$$ | 208.980388 u | $$_{84}^{210}Po$$ | 209.982876 u |
(1 u = 932 MeV/c2)
The kinetic energy (in keV) of the alpha particle, when the nucleus $$_{84}^{210}Po$$ at rest undergoes alpha decay, is
A right-angled prism of refractive index $$\mu$$1 is placed in a rectangular block of refractive index $$\mu$$2, which is surrounded by a medium of refractive index $$\mu$$3, as shown in the figure. A ray of light e enters the rectangular block at normal incidence. Depending upon the relationships between $$\mu$$1, $$\mu$$2 and $$\mu$$3, it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'.
Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:
| List I | List II | ||
|---|---|---|---|
| P. | $$e \to f$$ |
1. | $${\mu _1} > \sqrt 2 {\mu _2}$$ |
| Q. | $$e \to g$$ |
2. | $${\mu _2} > {\mu _1}$$ and $${\mu _2} > {\mu _3}$$ |
| R. | $$e \to h$$ |
3. | $${\mu _1} = {\mu _2}$$ |
| S. | $$e \to i$$ |
4. | $${\mu _2} < {\mu _1} < \sqrt 2 {\mu _2}$$ and $${\mu _2} > {\mu _3}$$ |
One mole of a monatomic ideal gas is taken along two cyclic processes E $$\to$$ F $$\to$$ G $$\to$$ E and E $$\to$$ F $$\to$$ H $$\to$$ E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.
Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists :
| List I | List II | ||
|---|---|---|---|
| P. | $$G \to E$$ |
1. | 160$${P_0}{V_0}$$ln2 |
| Q. | $$G \to H$$ |
2. | 36$${P_0}{V_0}$$ |
| R. | $$F \to H$$ |
3. | 24$${P_0}{V_0}$$ |
| S. | $$F \to G$$ |
4. | 31$${P_0}{V_0}$$ |