81. The average binding energy of a nucleon inside an atomic nucleus is about

1. 1. 8 MeV

   
   
   

   2. 8 eV

   
   
   

   3. 8 J

   
   
   

   4. 8 ergs

   
   
   

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1. View Hint View Answer Discuss in Forum

   Average B.E./nucleon in nuclei is of the order of 8 MeV.

   Correct Option: A

   Average B.E./nucleon in nuclei is of the order of 8 MeV.

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82. Radioactive material 'A' has decay constant '8 λ' and material 'B' has decay constant 'λ'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be

    	1	?
    	e

1. 1. 1

      7λ

   
   
   

   2. 1

      8λ

   
   
   

   3. 1

      9λ

   
   
   

   4. 1

      λ

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given,
   λ_A = 8λ, λ_B = λ
   

   NB =	NA
   	e

   
   ⇒ N₀e^-λB^t
   

   = N0	e-λAt
   	e

   
   e^-λt = e^-8λte^-1
   e^λt = e^{8λt - 1}
   Comparing both side powers
   -λt = -8λt - 1
   - 1 = 7λt
   

   t = -	1
   	7λ

   
   The best possible answer is
   

   t =	1
   	7λ

   Correct Option: A

   Given,
   λ_A = 8λ, λ_B = λ
   

   NB =	NA
   	e

   
   ⇒ N₀e^-λB^t
   

   = N0	e-λAt
   	e

   
   e^-λt = e^-8λte^-1
   e^λt = e^{8λt - 1}
   Comparing both side powers
   -λt = -8λt - 1
   - 1 = 7λt
   

   t = -	1
   	7λ

   
   The best possible answer is
   

   t =	1
   	7λ

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83. A radio isotope ‘X’ with a half life 1.4 × 10⁹ years decays to ‘Y’ which is stable. A sample of the rock from a cave was found to contain ‘X’ and ‘Y’ in the ratio 1 : 7. The age of the rock is :

1. 1. 1.96 × 10⁹ years

   
   
   

   2. 3.92 × 10⁹ years

   
   
   

   3. 4.20 × 10⁹ years

   
   
   

   4. 8.40 × 10⁹ years

   
   
   

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1. View Hint View Answer Discuss in Forum

   As	Nx	=	1	(Given)
   	Ny		7

   
   

   ⇒	Nx	=	1
   	Nx + Ny		8

   
   

   =		1		3
   		2

   
   Therefore, age of the rock
   t = 3T_1/2 = 3 × 1.4 × 10⁹ yrs = 4.2 × 10⁹ yrs.

   Correct Option: C

   As	Nx	=	1	(Given)
   	Ny		7

   
   

   ⇒	Nx	=	1
   	Nx + Ny		8

   
   

   =		1		3
   		2

   
   Therefore, age of the rock
   t = 3T_1/2 = 3 × 1.4 × 10⁹ yrs = 4.2 × 10⁹ yrs.

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84. The half life of a radioactive isotope ‘X’ is 20 years. It decays to another element ‘Y’ which is stable. The two elements ‘X’ and ‘Y’ were found to be in the ratio of 1 : 7 in a sample of a the given rock. The age of the rock is estimated to be

1. 1. 60 years

   
   
   

   2. 80 years

   
   
   

   3. 100 years

   
   
   

   4. 40 years

   
   
   

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1. View Hint View Answer Discuss in Forum

   The value of x is 1/8
   

   =	X0	=	X0
   	8		23

   
   ⇒ t = 3T = 3 × 20 = 60 years
   Hence the estimated age of the rock is 60 years
   

   ALTERNATE	X	→	Y0
   att = 0	N0		O
   att = t	N		N0 - N

   
   

   	N	=	1	=	N	=	1
   	N0 - N		7		N0		8

   
   t = 3T
   = 3 × 20 = 60 years

   Correct Option: A

   The value of x is 1/8
   

   =	X0	=	X0
   	8		23

   
   ⇒ t = 3T = 3 × 20 = 60 years
   Hence the estimated age of the rock is 60 years
   

   ALTERNATE	X	→	Y0
   att = 0	N0		O
   att = t	N		N0 - N

   
   

   	N	=	1	=	N	=	1
   	N0 - N		7		N0		8

   
   t = 3T
   = 3 × 20 = 60 years

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85. α-particles, β-particles and γ-rays are all having same energy. Their penetrating power in a given medium in increasing order will be

1. 1. β, γ, α

   
   
   

   2. γ, α, β

   
   
   

   3. α, β, γ

   
   
   

   4. β, α, γ

   
   
   

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1. View Hint View Answer Discuss in Forum

   Increasing order of penetrating power :
   <α <β <γ
   For same energy, lighter particle has higher penentrating power.

   Correct Option: C

   Increasing order of penetrating power :
   <α <β <γ
   For same energy, lighter particle has higher penentrating power.

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