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JEE Advance - Physics (2013 - Paper 2 Offline - No. 16)

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 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 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 nucleus $$_3^6Li$$ can emit an alpha particle.
the nucleus $$_{84}^{210}Po$$ can emit a proton.
deuteron and alpha particle can undergo complete fusion.
the nuclei $$_{30}^{70}Zn$$ and $$_{34}^{82}Se$$ can undergo complete fusion.

Explanation

We have

$$m(_1^2H) + m(_2^4He) = 2.014102 + 4.002603 = 6.016705\,u$$

$$m(_3^6Li) = 6.015123\,u$$

$${m_1} + {m_2} > M$$

Thus, option (A) is wrong.

$$m(_1^1H) + m(_{83}^{209}Bi) = 1.007825\,u + 208.980388\,u = 209.988213\,u$$

$$m(_{84}^{210}Po) = 209.982876\,u$$

$${m_1} + {m_2} > M$$

Thus, option (B) is wrong.

$$m(_1^2H) + m(_2^4He) = 2.014102\,u + 4.002603\,u = 6.016705\,u$$

$$_3^6Li = 6.015123\,u$$

$$({m_3} + {m_4}) > M'$$

Thus, option (C) is correct. Therefore, deuteron and alpha particle can go complete fusion.

$$m(_{30}^{70}Zn) + _{34}^{82}Se = 69.925325\,u + 81.916709\,u = 151.842034\,u$$

$$_{64}^{152}Gd = 151.919803\,u$$

$${m_3} + {m_4} < M'$$

Thus, option (D) is wrong.

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