The wavelength of $K_{\alpha }$ X-rays for lead isotopes $P{b}^{208},<mspace\; width="1em"></mspace>P{b}^{206},<mspace\; width="1em"></mspace>P{b}^{204}<mspace\; width="1em"></mspace>are<mspace\; width="1em"></mspace>{\lambda }_1,<mspace\; width="1em"></mspace>{\lambda }_2<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>{\lambda }_3$ 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 

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 

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 

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. $X{e}_{{}_{54}}^{143}+3<mspace\; width="1em"></mspace>n_0^1$ 

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. $2^{1/3}<mspace\; width="1em"></mspace>:<mspace\; width="1em"></mspace>1$ 

2. $1<mspace\; width="1em"></mspace>:<mspace\; width="1em"></mspace>2^{1/3}$ 

3. $3^{1/2}<mspace\; width="1em"></mspace>:<mspace\; width="1em"></mspace>1$

4. $1<mspace\; width="1em"></mspace>:<mspace\; width="1em"></mspace>3^{1/2}$

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