An $\alpha -$particle of energy 5 MeV is scattered through $180°$ by a fixed uranium nucleus. The distance of closest approach is of the order

1. ${10}^{-10}<mspace\; width="1em"></mspace>m$ 

2. ${10}^{-13}<mspace\; width="1em"></mspace>m$ 

3. ${10}^{-14}<mspace\; width="1em"></mspace>m$ 

4. ${10}^{-16}<mspace\; width="1em"></mspace>m$

The wavelength of K_a X-rays produced by an X-ray tube is 0.76 $\stackrel{\circ }{A}$. Find the atomic number of the anode material of the tube?

1. 41

2. 30

3. 20

4. 10

Energy levels A, B, C of a certain atom correspond to increasing values of energy i.e. $E_A<E_B<E_C.$ If ${\lambda }_1,<mspace\; width="1em"></mspace>{\lambda }_2,<mspace\; width="1em"></mspace>{\lambda }_3$ are the wavelengths of the radiation corresponding to the transitions C to B, B to A and C to A respectively, which of the following relation is correct?

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

2. ${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$

3. ${\lambda }_1+{\lambda }_2+{\lambda }_3=0$ 

4. ${\lambda }_3^2={\lambda }_1^2+{\lambda }_2^2$

The velocity of the electron in the ground state (H - atom) is 

1. $2.18\times {10}^5<mspace\; width="1em"></mspace>m/s$   

2. $2.18\times {10}^6<mspace\; width="1em"></mspace>m/s$

3. $2.18\times {10}^7<mspace\; width="1em"></mspace>m/s$   

4. $2.18\times {10}^8<mspace\; width="1em"></mspace>m/s$

Which of the following transitions gives photon of maximum energy?

1. n = 1 to n = 2 

2. n = 2 to n = 1

3. n = 2 to n = 6 

4. n = 6 to n = 2

When electron jumps from n = 4 to n = 2 orbit, we get [2000]

1. second line of Lyman series

2. second line of Balmer series

3. second line of Paschen series

4. an absorption line of Balmer series

In terms of Bohr radius $a_0$, the radius of the second Bohr orbit of a hydrogen atom is given by [1992]

1. 4$a_0$ 

2. 8$a_0$ 

3. $\sqrt{2}$$a_0$     

4. 2$a_0$

A diatomic molecule is made of two masses $m_1<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>m_2$ which are separated by a distance r.  If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by (n is an integer):

1. $\frac{{\left(m_1+m_2\right)}^2{n}^2{h}^2}{2m_1^2{m}_2^2{r}^2}$     

2. $\frac{n^2{h}^2}{2{\mathrm{\pi }}^2(m_1^{}+m_2^{})r^2}$

3. $\frac{2n^2{h}^2}{(m_1^{}+m_2^{})r^2}$   

4. $\frac{\left(m_1+m_2\right)n^2{h}^2}{8{\mathrm{\pi }}^2{m}_1^{}{m}_2^{}{r}^2}$

In the Bohr's hydrogen atom model, the radius of the stationary orbit is directly proportional to (n = principal quantum number) [CBSE PMT 1996; AIIMS 199; DCE 2002; AMU (med.) 2010)

1. $n^{-1}$   

2. n

3. $n^{-2}$ 

4. $n^2$