Half Life and Average Life

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

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

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

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

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

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

Q. A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

1. 6h
2. 12 h
3. 24 h
4. 128 h

Q. A certain substance decays to ${\frac{1}{64}}^{th}$ of its initial activity in $24$ days. The half-life of the substance will be

1. $6$ days
2. $4$ days
3. $3$ days
4. $2$ days

Q. Starting with a sample of pure ${}^{66}Cu,\frac{7}{8}$ of it decays into $Zn$ in $15$ min. The corresponding half- life is

1. $15\text{min}$
2. $5\text{min}$
3. $10\text{min}$
4. $7\frac{1}{2}\text{min}$

Q.

What is a decay constant?

Q.

A car travels a distance A to B at a speed of is $40\text{\hspace{0.17em}km/hr}$ and returns to A at a speed of $30\text{\hspace{0.17em}km/hr}$. The average velocity (in km/hr) for the whole journey is,

1. $34.3$

2. $0$

3. $35$

4. $36.3$

Q. The half life of a radioactive substance is $20$ minutes. Then the approximate time interval $(t_2-t_1)$ between the time $t_2$ when ${\frac{2}{3}}^{rd}$ of it has decayed and time $t_1$ when ${\frac{1}{3}}^{rd}$ of it has decayed is

1. $7min$
2. $14min$
3. $20min$
4. $28min$

Q. A freshly prepared sample of a radioisotope of half-life 1386 s has activity ${10}^3$ disintegrations per second. Given that ln 2 = 0.693, find the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample.___

Q. A radioactive substance has a half life of 60 minutes. After 3 hours, the percentage of atom that have decayed would be

1. 12.5%
2. 87.5%
3. 8.5%
4. 25.1%

Q. Tritium has a half life of 12.5 years undergoing beta decay. What fraction of sample of pure tritium will decay in 50 years?

1. $\frac{3}{4}$
2. $\frac{15}{16}$
3. $\frac{63}{64}$
4. $\frac{7}{8}$

Q.

The fraction of atoms of radioactive element that decays in 6 days is $\frac{7}{8}$. The fraction that decays in 10 days will be

1. $\frac{15}{16}$
2. $\frac{77}{80}$
3. $\frac{71}{80}$
4. $\frac{31}{32}$

Q. The fossil bone has a ${}^{14}C{:}^{12}C$ ratio, which is $\left(\frac{1}{16}\right)$ of that in a living animal bone. If the half of ${}^{14}C$ is $5730$ years, then the age of the fossil (in years) is :-

Q. A radioactive material decrease by simultaneous emissions of two particles with half life 1620 years and 810 years the time after which 1/4 th of the material remained is

Q. The half-life of ${}^{198}Au$ is 2.7 days. Calculate the decay constant.Take atomic weightof ${}^{198}Au$ to be 198 g $mo{l}^{-1}$

1. 
2. 
3. 
4. 

Q. The kinetic energy (in keV) of the alpha particle, when the nucleus ${}_{84}^{210}Po$ at rest undergoes alpha decay, is

1. $5707$
2. $5818$
3. $5422$
4. $5319$

Q.

The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive present with the stable carbon isotope . When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life (5730 years) of, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.

Q.

The half-life of cobalt-60 is 5.25 yrs. After how long does its activity reduce to about one eight of its original value?

1. 5.25 years

2. 10.50 years

3. 15.75 years

4. 21 years

Q. The kinetic energy of a neutron beam is 0.0837 eV. The half-life of neutrons is 693s and the mass of neutrons is $1.675\times {10}^{-27}$ kg. The fraction of decay in travelling a distance of 40m will be

1. ${10}^{-3}$
   
2. ${10}^{-4}$
   
3. ${10}^{-5}$
   
4. ${10}^{-6}$

Q.

The decay constant of ${}^{238}\text{U}$ is $4.9\times {10}^{-18}{S}^{-1}$ (a) What is the average - life of ${}^{238}\text{U}$ ? (b) What is the half-life of ${}^{238}\text{U}$ ? (c) By what factor does the activity of a ${}^{238}\text{U}$ sample decrease in $9\times {10}^9$ years ?

Q. Equal masses of two samples of charcoal A and B are burnt separately and the resulting carbon dioxide are collected in two vessels. The radioactivity of ${}^{14}C$ is measured for both the gas samples. The gas from the charcoal A gives 2100 counts per week and the gas from the charcoal B gives 1400 counts per week. Find the age difference between the two samples. Half-life of ${}^{14}C$ = 5730 y.

1. 2500 Years
2. 3352 Years
3. 4567 Years
4. 2392 Years

Q.

A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample ? (b) What is its half-life ?

Q. The half-life of 9038 Sr is 28 years. What is the disintegration rate of15 mg of this isotope?

Q. The normal activity of living carbon-containing matter is found tobe about 15 decays per minute for every gram of carbon. This activityarises from the small proportion of radioactive 146 C present with thestable carbon isotope 126 C . When the organism is dead, its interactionwith the atmosphere (which maintains the above equilibrium activity)ceases and its activity begins to drop. From the known half-life (5730years) of 146 C , and the measured activity, the age of the specimencan be approximately estimated. This is the principle of 146C dating used in archaeology. Suppose a specimen from Mohenjodaro givesan activity of 9 decays per minute per gram of carbon. Estimate theapproximate age of the Indus-Valley civilisation.

Q.

The probability that a certain radioactive atom would get disintegrated in a time equal to the mean life of the radioactive sample is:

1. 0.37

2. 0.50

3. 0.63

4. 0.67

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

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

Q. A radioactive element emits 200 particles per second. After three hours 25 particles per second are emitted. The half-life period of element will be

1. $50\text{minutes}$
2. $60\text{minutes}$
3. $70\text{minutes}$
4. $80\text{minutes}$

Q. Half-lives of two radioactive substances A and B are, respectively, $20$ min and $40$ min. Initially, the samples of A and B have equal number of nuclei. After $80$ min, the ratio of the remaining number of A and B nuclei is

1. $4:1$
2. $1:4$
3. $1:16$
4. $1:1$