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. 

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 $P{b}^{208},<mspace\; width="1em"></mspace>P{b}^{206},<mspace\; width="1em"></mspace>P{b}^{204}<mspace\; width="1em"></mspace>are<mspace\; width="1em"></mspace>{\lambda }_1,<mspace\; width="1em"></mspace>{\lambda }_2<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>{\lambda }_3$ 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