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

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

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

Given a sample of Radium-226 having half-life of 4 days. Find the probability, a nucleus disintegrates after 2 half lives [IIT-JEE 2006]

1. 1 

2. 1/2 

3. 1.5 

4. 3/4

Complete the equation for the following fission process-

$U_{92}^{235}+n_0^1\to S{r}_{38}^{90}+........$  

1. $X{e}_{{}_{54}}^{143}+3 n_0^1$ 

2. $X{e_{{}_{54}}^{145}}^{}$

3. $X{e_{{}_{57}}^{142}}^{}$ 

4. $X{e_{{}_{54}}^{142}}^{}+n_0^1$

A nucleus ruptures into two nuclear parts which have their velocity ratio equal to 2:1. What will be the ratio of their nuclear size (nuclear radius) ? 

1. $2^{1/3} : 1$ 

2. $1 : 2^{1/3}$ 

3. $3^{1/2} : 1$

4. $1 : 3^{1/2}$

The half-life of a radioactive material is 3h. If the initial amount is 300g, then after 18h, it will remain

1. 4.68 g 

2. 46.8 g

3. 9.375 g 

4. 93.75 g