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JEE Advance - Physics (2013 - Paper 2 Offline - No. 17)

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 kinetic energy (in keV) of the alpha particle, when the nucleus $$_{84}^{210}Po$$ at rest undergoes alpha decay, is
5319
5422
5707
5818

Explanation

The alpha decay of $$_{84}^{210}Po$$ is given by

$$_{84}^{210}Po \to _{82}^{206}Pb + _2^4He$$

The energy released during this process is

$$Q = ({M_{Po}} - {M_{Pb}} - {M_{He}}){c^2}$$

$$ = (209.982876 - 205.974455 - 4.002603)\,u \times {c^2}$$

$$ = (0.005818\,u){c^2} = (0.005818\,u) \times 932\,MeV$$

$$ = 5.422\,MeV = 5422\,keV$$

Kinetic energy of a particle, $${K_\alpha } = {{(A - 4)Q} \over A}$$

$${K_\alpha } = {{(210 - 4)} \over {210}} \times 5422\,keV = {{206} \over {210}} \times 5422\,keV = 5319\,keV$$

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