A radioactive material has mean-lives of 1620 yr and 520 yr for $\alpha$ and $\beta$-emission. The material decays by simultaneous $\alpha$ and $\beta$-emission. The time in which 1/4th of the material remains intact is 

1. 4675 yr 

2. 720 yr

3. 545 yr 

4. 324 yr

The radioactivity of an element becomes $\frac{1}{64}th$ of its original value in 60 seconds. Then the half value period is

1. 5 sec 

2. 10 sec 

3. 20 sec

4. 30 sec

A nucleus of ${}_{84}{}^{210}Po$ originally at rest emits $\alpha$ particle with speed $\nu$. What will be the recoil speed of the daughter necleus. [DCE 2002]

1. 4$\nu$ / 206

2. 4$\nu$ / 214

3. $\nu$ / 206 

4. $\nu$ / 214

An atom of mass number 15 and atomic number 7 captures an $\alpha$-particle and then emits a proton. The mass number and atomic number of the resulting product will respectively be

1. 14 and 2

2. 15 and 3

3. 16 and 4 

4. 18 and 8

The wavelength of $K_{\alpha }$ X-rays for lead isotopes $P{b}^{208}, P{b}^{206}, P{b}^{204} are {\lambda }_1, {\lambda }_2 and {\lambda }_3$ respectively. Then

1. ${\lambda }_1={\lambda }_2>{\lambda }_3$   

2. ${\lambda }_1>{\lambda }_2>{\lambda }_3$

3. ${\lambda }_1<{\lambda }_2<{\lambda }_3$ 

4. ${\lambda }_2={\lambda }_1={\lambda }_3$

Solar energy is mainly caused due to [2003]

1. fusion of protons during synthesis of heavier elements

2. gravitational contraction

3. burning of hydrogen in the oxygen

4. fission of uranium present in the sun

A sample of radioactive elements contains $4\times {10}^{10}$ active nuclei. If half-life of element is 10 days, then the number of decayed nuclei after 30 days is 

1. $0.5\times {10}^{10}$   

2. $2\times {10}^{10}$

3. $3.5\times {10}^{10}$

4. $1\times {10}^{10}$

A and B are two radioactive substances whose half-lives are 1 and 2 years respectively. Initially 10 g of A and 1 g of B is taken. The time (approximate) after which they will have the same quantity remaining is:

1. 6.62 yr

2. 5 yr   

3. 3.2 yr 

4. 7 yr

In a radioactive decay process, the negatively charged emitted $\beta$-particles are:

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 means lives in [CBSE PMT/PDT 2003]

1. 3.70 gm

2. 6.30 gm

3. 1.35 gm 

4. 2.50 gm