Half Life and Average Life

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. If 20 gm of a radioactive substance due to radioactive decay reduces to 10 gm in 4 minutes, then in what time 80 gm of the same substance will reduce to 10 gm

1. In 8 minutes
2. In 12 minutes
   
3. In 16 minutes
4. In 20 minutes

Q. The radioactive element which is used to find the age of the fossil is

1. C-14
2. U-234
3. U-238
4. Po-94

Q. From a newly formed radioactive substance (Half-life 2 hours), the intensity of radiation is 64 times the permissible safe level. The minimum time after which work can be done safely from this source is

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

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

Q. ${}_{87}{Ra}^{221}$ is a radioactive substance having half life of 4 days. Find the probability that a nucleus undergoes decay after two half lives
[IIT-JEE-2006]

1. 1
2. $\frac{1}{2}$
3. $\frac{3}{4}$
4. $\frac{1}{4}$

Q. Half-life of a substance is 20 minutes. What is the time between 33% decay and 67% decay

1. 40 minutes
2. 20 minutes
3. 30 minutes
4. 25 minutes

Q. The decay constant of ${}^{238}U$ is $1.54\times {10}^{-10}y{r}^{-1}$. What will be the average life of a sample of ${10}^{20}$ such ${}^{238}U$ nuclei?

1. 3.25 billion years
2. 6.49 million years
3. 3.25 million years
4. 6.49 billion years

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. 0.63

3. 0.50

4. 0.67

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. $2.9\times {10}^{-10}{S}^{-1}$
2. $2.9\times {10}^{-8}{S}^{-1}$
3. $2.9\times {10}^{-6}{S}^{-1}$
4. $2.9\times {10}^{-4}{S}^{-1}$

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

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

Q. The radioactive element which is used to find the age of the fossil is

1. C-14
2. U-234
3. U-238
4. Po-94

Q.

The mean lives of a radioactive substance are 1620 and 405 years for $\alpha$-emission and $\beta$-emission respectively. Find out the time during which three fourth of a sample will decay if it is decaying both by $\alpha$-emission and $\beta$-emission simultaneously.

1. 449 years

2. 440 years

3. 520 years

4. 549 years

Q. ${}_{87}{Ra}^{221}$ is a radioactive substance having half life of 4 days. Find the probability that a nucleus undergoes decay after two half lives
[IIT-JEE-2006]

1. 1
2. $\frac{1}{2}$
3. $\frac{3}{4}$
4. $\frac{1}{4}$

Q. What is the approximate age of the ancient tree sample if specific activity of $C-14$ in it is $\frac{1}{4}$ of the activity of newly felt trees? Half-life of $C-14$ is 5570 years.

1. 11, 140 years
2. 5570 years
3. 16, 710 years
4. 2785 years

Q.

In one average-life,

1. half the active nuclei decay

2. less than half the active nuclei today

3. more than half the active nuclei decay

4. all the nuclei decay

Q. The half−value period of a synthetic molecule is given to be 26.8 minutes. The mass of One curie of this molecule is (1 curie $=3.71\times {10}^{10}dps$ and molecular mass of molecule $=214\text{g}$)

1. $3.71\times {10}^{10}g$
2. $3.71\times {10}^{10}g$
3. $8.61\times {10}^{10}g$
4. $3.064\times {10}^{-8}g$

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. In one average life

1. Half the active nuclei decay
2. Less than half the active nuclei decay
3. More than half the active nuclei decay
4. All the nuclei decay

Q. Ten grams of ${}^{60}Co$ kept in an open container $\beta$ decays with a half-life of 270 days. The decay products are constantly flushed out. The weight of the material inside the container after 540 days will be very nearly:

1. 10 g
2. 5 g
3. 2.5 g
4. 1.25 g