Half Life and Average Life

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

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. 3.70 gm
3. 6.30 gm
4. 1.35 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. $25s^{-1}$
2. $80s^{-1}$
3. $625s^{-1}$
4. $20s^{-1}$

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. 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. ${}_{87}{Ra}^{221}$ 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. 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.

Age of a fossil can be estimated by tracing the amount of

1. normal carbon

2. radioactive carbon

3. radioactive oxygen

4. normal oxygen

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

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

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. 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 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 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. 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 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 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. 200 years
4. 250 years

Q. Is the following relation true or false: $t_{\frac{1}{2}}=2\times t_{\frac{1}{4}}$.

1. True
2. False

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. 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