6. A nucleus _ZX^A has mass represented by M(A, Z). If M_p and M_n denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then

1. 1. B.E. = [ZM_p + (A – Z)M_p – M(A, Z)]c²

   
   
   

   2. B.E. = [ZM_p + ZMn – M(A, Z)]c²

   
   
   

   3. B.E. = M(A, Z) – ZM_p – (A – Z)M_n

   
   
   

   4. B.E. = [M(A, Z) – ZM_p – (A – Z)M_n]c²

   
   
   

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1. View Hint View Answer Discuss in Forum

   The difference in mass of a nucleus and its constituents, ΔM, is called the mass defect and is given by
   ΔM = [ZM_p + (A - Z)M_n] - M
   and binding energy = ΔMc²
   [{ZM_p + (A - Z)M_n} - M]c²

   Correct Option: A

   The difference in mass of a nucleus and its constituents, ΔM, is called the mass defect and is given by
   ΔM = [ZM_p + (A - Z)M_n] - M
   and binding energy = ΔMc²
   [{ZM_p + (A - Z)M_n} - M]c²

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7. ​If M (A; Z), M_p and M_n denote the masses of the nucleus _ZX^A proton and neutron respectively  in units of u ( 1u = 931.5 MeV/c²) and  BE represents its bonding energy in MeV, then

1. 1. M (A, Z) = ZM_p + (A – Z) M_n –BE/c²

   
   
   

   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 + BE/c²

   
   
   

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1. View Hint View Answer Discuss in Forum

   Mass defect = ZM_p + (A –Z)M_n–M(A,Z)
   

   or,	B.E
   	c2

   
   = ZM_p + (A–Z) M_n–M(A,Z) ​
   

   ∴ M (A, Z) = ZMp + (A–Z)Mn –	B.E
   	c2

   Correct Option: A

   Mass defect = ZM_p + (A –Z)M_n–M(A,Z)
   

   or,	B.E
   	c2

   
   = ZM_p + (A–Z) M_n–M(A,Z) ​
   

   ∴ M (A, Z) = ZMp + (A–Z)Mn –	B.E
   	c2

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8. A nucleus of mass M emits a photon of frequency ν and the nucleus recoils. The recoil energy will be

1. 1. Mc² – hν ​

   
   
   

   2. h²ν² / 2Mc²

   
   
   

   3. zero

   
   
   

   4. hν

   
   
   

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1. View Hint View Answer Discuss in Forum

   Momentum
   

   Mu =	E	=	hv
   	c		c

   
   Recoil energy
   

   Correct Option: B

   Momentum
   

   Mu =	E	=	hv
   	c		c

   
   Recoil energy
   

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9. How does the binding energy per nucleon vary with the increase in the number of nucleons?

1. 1. ​Increases continuously with mass number

   
   
   

   2. Decreases continuously with mass number ​

   
   
   

   3. First decreases and then increases with increase in mass number

   
   
   

   4. First increases and then decreases with increase in mass number

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   From the graph of BE/A versus mass number A  it is clear that, BE/A first increases and then decreases with increase in mass number.

   Correct Option: D

   
   From the graph of BE/A versus mass number A  it is clear that, BE/A first increases and then decreases with increase in mass number.

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10. The power obtained in a reactor using U²³⁵ disintegration is 1000 kW. The mass decay of U²³⁵ per hour is​​​

1. 1. 10 micro gram ​

   
   
   

   2. 20 micro gram ​

   
   
   

   3. 40 micro gram

   
   
   

   4. 1 micro gram

   
   
   

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1. View Hint View Answer Discuss in Forum

   E = mc²
   

   m =	E
   	c2

   
   So, mass decay per second
   

   	dm	=	1		dE	=	1	(Power in watt)
   	dt		c2		dt		c2

   
   

   =	1	× 1000 × 103
   	(3 × 108)2

   
   and mass decay per hour
   

   =	dm	× 60 × 60
   	dt

   
   

   =	1	× 106 × 3600
   	(3 × 108)2

   
   = 4 × 10^–8 kg ​= 40 micro gram

   Correct Option: C

   E = mc²
   

   m =	E
   	c2

   
   So, mass decay per second
   

   	dm	=	1		dE	=	1	(Power in watt)
   	dt		c2		dt		c2

   
   

   =	1	× 1000 × 103
   	(3 × 108)2

   
   and mass decay per hour
   

   =	dm	× 60 × 60
   	dt

   
   

   =	1	× 106 × 3600
   	(3 × 108)2

   
   = 4 × 10^–8 kg ​= 40 micro gram

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