Nuclei

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to ( 116 )th of its initial value?

1. 40 minutes
2. 60 minutes
3. 80 minutes
4. 20 minutes

Given below are two statements In the light of the above statements, choose the most appropriate answer from the options given below :

1. Statement I is incorrect but statement II is correct
2. Both statement I and statement II are correct
3. Both statement I and statement II are incorrect
4. Statement I is correct but statement II is incorrect

At any instant, two elements X1 and X2 have same number of radioactive atoms. If the decay constant of X1 and X2 are 10 and respectively, then the time when the ratio of their atoms becomes 1e respectively will be :

1. 15
2. 111
3. 19
4. 16

The half life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be :

1. 23 2
2. 12
3. 12 2
4. 23

For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is

1. 20
2. 10
3. 30
4. 15

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

1. 17
2. 18
3. 19
4. 1

The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is

1. 15
2. 30
3. 45
4. 60

A radioactive 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. 1.96 109 years
2. 3.92 109 years
3. 4.20 109 years
4. 8.40 109 years

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 1 : 7 in a sample of a given rock. The age of the rock is estimated to be

1. 80 years
2. 100 years
3. 40 years
4. 60 years

The half life of a radioactive nucleus is 50 days. The time interval (t2 - t1) between the time t2 when 23 of it has decayed and the time t1 when 13 of it had decayed is

1. 30 days
2. 50 days
3. 60 days
4. 15 days

A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A1 and 160 g of A2. The amount of the two in the mixture will become equal after

1. 60 s
2. 80 s
3. 20 s
4. 40 s

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0, the number of P species is 4N0 and that of Q is N0. Half-life of P (for conversion to R) is 1 minute whereas that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be

1. 2N0
2. 3N0
3. 9N02
4. 5N02

The half life of a radioactive isotope X is 50 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 : 15 in a sample of a given rock. The age of the rock was estimated to be

1. 150 years
2. 200 years
3. 250 years
4. 100 years

The decay constant of a radioisotope is . If A1 and A2 are its activities at times t1 and t2 respectively, the number of nuclei which have decayed during the time (t1 - t2)

1. A1t1 - A2t2
2. A1 - A2
3. (A1 - A2)/
4. (A1 - A2)

The activity of a radioactive sample is measured as N0 counts per minute at t = 0 and N0/e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is

1. e 25
2. 5 e 2
3. 5 10 2
4. 5 e 2

Two radioactive materials X1 and X2 have decay constants 5 and respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that of X2 will be 1e after a time

1. 14
2. e
4. 12

Two radioactive substances A and B have decay constants 5 and respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be ( 1e )2 after a time interval

1. 4
2. 2
3. 12
4. 14

In a radioactive material the activity at time t1 is R1 and at a later time t2, it is R2. If the decay constant of the material is , then

1. R1 = R2
2. R1 = R2 e- (t1 - t2)
3. R1 = R2 e (t1 - t2)
4. R1 = R2(t2/t1).

The half life of radium is about 1600 years. Of 100 g of radium existing now, 25 g will remain unchanged after

1. 4800 years
2. 6400 years
3. 2400 years
4. 3200 years

A sample of radioactive element has a mass of 10 g at an instant t = 0. The approximate mass of this element in the sample after two mean lives is

1. 1.35 g
2. 2.50 g
3. 3.70 g
4. 6.30 g

A sample of radioactive element containing 4 1016 active nuclei. Half-life of element is 10 days, then number of decayed nuclei after 30 days

1. 0.5 1016
2. 2 1016
3. 3.5 1016
4. 1 1016

Half life of a radioactive element is 12.5 hours and its quantity is 256 g. After how much time its quantity will remain 1 g?

1. 50 h
2. 100 h
3. 150 h
4. 200 h

The relation between and T1/2 is ( T1/2 half-life)

1. T1/2 = 2
2. T1/2 2 =
3. T1/2 = 1
4. ( + T1/2) = 2