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$${P_0}{V_0}$$ |
Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists :
| List I | List II | ||
|---|---|---|---|
| P. | Alpha decay | 1. | $$_8^{15}O \to _7^{15}N + ...$$ |
| Q. | $${\beta ^ + }$$ decay | 2. | $$_{91}^{238}U \to _{90}^{234}Th + ...$$ |
| R. | Fission | 3. | $$_{83}^{185}Bi \to _{82}^{184}Pb + ...$$ |
| S. | Proton emission | 4. | $$_{94}^{239}Pu \to _{57}^{140}La + ...$$ |