In a radioactive substance at t = 0, the number of atoms is 8×104, its half-life period is 3 yr. The number of atoms equal to 1×104 will remain after an interval of:

1. 9 yr

2. 8 yr 

3. 6 yr 

4. 24 yr

Subtopic:  Radioactivity (OLD NCERT) |
 75%
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PMT - 2010
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The half-life of radium is 1622 years. How long will it take for seven-eighth of a given amount of radium to decay

1. 3244 years

2. 6488 years

3. 4866 years

4. 811 years

Subtopic:  Radioactivity (OLD NCERT) |
 72%
From NCERT
PMT - 1999
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In a radioactive sample the fraction of initial number of radioactive nuclei, which remains undecayed after n mean lives is:

1. 1en 

2.  en   

3. 1-1en 

4. 1e-1n

Subtopic:  Radioactivity (OLD NCERT) |
 54%
From NCERT
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The activity of a radioactive sample is measured as 9750 counts/min at t = 0 and as 975 counts/min at t = 5 min. The decay constant is approximately:

1. 0.922/min           

2. 0.691/min         

3. 0.461/min           

4. 0.230/min

Subtopic:  Radioactivity (OLD NCERT) |
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At time t = 0, N1 nuclei of decay constant λ1 and N2 nuclei of decay constant λ2 are mixed. The decay rate of the mixture is:

1. -N1N2e-λ1+λ2t 

2. -N1N2 e-λ1+λ2t 

3. -N1λ1e-λ1t + N2λ2e-λ2t 

4. -N1λ1N2λ2e-λ1+λ2t

Subtopic:  Radioactivity (OLD NCERT) |
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The half-life period of a radioactive substance is 6 h.  If after 24 h, activity is 0.01 μCi, what was the initial activity? 

1. 0.04 μCi 

2. 0.08 μCi

3. 0.24 μCi 

4. 0.16 μCi

Subtopic:  Radioactivity (OLD NCERT) |
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The radioactivity of a sample is A1 at a time t1 and A2 at time t2.  If the mean life of the specimen is T, the number of atoms that have disintegrated in the time interval of t2-t1 is:

1. A1-A2 

2. A1-A2T

3. A1-A2T

4. A1t1-A2t2

Subtopic:  Radioactivity (OLD NCERT) |
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The relationship between disintegration constant λ and half-life [T] will be:

1. λ=log10 2T 

2. λ=loge 2T

3. λ=Tloge 2   

4. λ=log2 eT

Subtopic:  Radioactivity (OLD NCERT) |
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Alpha particles are 

1. 2 free protons

2. helium atoms

3. singly ionized helium atoms

4. doubly ionised helium atoms

Subtopic:  Radioactivity (OLD NCERT) |
 61%
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A radioactive sample with a half-life of 1 month has the label: 'Activity = 2 microcurie on 1-8-1991'. What would be its activity two months earlier? 

1. 1.0 microcurie       

2. 0.5 microcurie           

3. 4 microcurie             

4. 8 microcurie

Subtopic:  Radioactivity (OLD NCERT) |
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