Half Life and Average Life

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. 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. 1620 year
3. 449 year
4. None of these

Q.

Calculate the time interval between $33\%$ decay and $67\%$ decay if half-life of a substance is $20$ minutes.

1. $40$ minutes

2. $20$ minutes

3. $60$ minutes

4. $13$ minutes

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. 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. 16 gm sample of a radioactive element is taken from Bombay to Delhi in 2 hour and it was found that 1 gm of the element remained (undisintegrated). Half life of the element is

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

Q.

The activity of a radioactive element reduces to $\frac{1}{16}$ of its original value in 36 years. The half life of the element is

1. 6 years

2. 9 years

3. 12 years

4. 18 years

Q.

A radioactive substance of half life 69.3 days is kept in a container. The time in which 80% of the substance will disintegrate will be [take ln(5) = 1.61]

1. 1.61 days

2. 16.1 days

3. 161 days

4. 1610 days

Q.

After $280$ days, the activity of a radioactive sample is $=6000\mathrm{dps}$. The activity reduces to$3000\mathrm{dps}$ after another $140$ days. What Is The initial activity of the sample in $\mathrm{dps}$?

Q.

Out of a radioactive sample 90% is found after one day. What percent of the original sample can be found after 2 days ?

1. 64%

2. 72%

3. 81%

4. 45%

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. Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II