A radioactive isotope X with a half-life of $1.37\times {10}^9$ years decays to Y which is stable. A sample of rock from the moon was found to contain both the elements X and Y which were in the ratio of 1 : 7. The age of the rock is
(a) $1.96\times {10}^8$ years         (b) $3.85\times {10}^9$ years
(c) $4.11\times {10}^9$years          (d) $9.59\times {10}^9$ years

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

The half-life of radium is 1620 years and its atomic weight is 226 kg per kilo mol. The number of atoms that will decay from its 1 gm sample per second will be:

(1) $3.61\times {10}^{10}$    

(2) $3.6\times {10}^{12}$

(3) $3.11\times {10}^{15}$     

(4) $31.1\times {10}^{15}$

(Avogardo's number N = $6.02\times {10}^{26}$ atoms/mol)

A radioactive material decays by simultaneous emission of two particles with respective half lives 1620 and 810 years. The time (in years) after which one- fourth of the material remains is 
(a) 1080         (b) 2430
(c) 3240         (d) 4860

The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Then

(1) X and Y have the same decay rate initially

(2) X and Y decay at the same rate always

(3) Y will decay at a faster rate than X

(4) X will decay at a faster rate than Y

For a substance, the average life for $\mathrm{\alpha }$-emission is 1620 years and for $\mathrm{\beta }$ emission is 405 years. After how much time the 1/4 of the material remains after simultaneous emission:

1. 1500 years            2. 300 years
3. 449 years              4. 810 years

A radioactive nucleus undergoes $\mathrm{\alpha }$-emission to form a stable element. What will be the recoil velocity of the daughter nucleus if v is the velocity of $\mathrm{\alpha }$-particle and A is the atomic mass of radioactive nucleus ?

1. $\frac{4\mathrm{V}}{\mathrm{A}-4}$             2. $\frac{2\mathrm{V}}{\mathrm{A}-4}$
3. $\frac{4\mathrm{V}}{\mathrm{A}+4}$             4. $\frac{2\mathrm{V}}{\mathrm{A}+4}$

The half-life of a radioactive substance is 20 minutes. The time between 20% and 80% decay will be: 

1. 20 minutes

2. 40 minutes

3. 30 minutes

4. 25 minutes

After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample in dps is

(1) 6000           

(2) 9000

(3) 3000           

(4) 24000

A radioactive sample is $\mathrm{\alpha }$-emitter with half life 138.6 days is observed by a student to have 2000 disintegration/sec. The number of radioactive nuclei for given activity are
(a) $3.45\times {10}^{10}$               (b) $1\times {10}^{10}$
(c) $3.45\times {10}^{15}$               (d) $2.75\times {10}^{11}$