Half Life and Average Life

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. The mean lives of a radioactive substance for $\alpha$ and $\beta$ emissions are 1620 years and 405 years respectively. After how much time will the activity be reduced to one fourth

1. 405 year
2. 449 year
3. None of these
4. 1620 year

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

Q. The counting rate observed from a radioactive source at t = 0 second was 1600 counts per second and at t = 8 seconds it was 100 counts per second. The counting rate observed as counts per second at t = 6 seconds will be

1. 400
2. 300
3. 200
4. 150

Q. At any instant the ratio of the amount of radioactive substances is 2 : 1. If their half lives be respectively 12 and 16 hours, then after two days, what will be the ratio of the substances

1. 1 : 1
2. 2 : 1
3. 1 : 2
4. 1 : 4

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

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

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. The count rate of a Geiger- Muller counter for the radiation of a radioactive material of half life of 30 minutes decreases to $5s^{-1}$ after 2 hours. The initial count rate was

1. $625s^{-1}$
2. $25s^{-1}$
3. $80s^{-1}$
4. $20s^{-1}$

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