If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength $\lambda$. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be

1.  $\frac{16}{25}\mathrm{\lambda }$

2.  $\frac{9}{16}\mathrm{\lambda }$

3.  $\frac{20}{7}\mathrm{\lambda }$

4.  $\frac{20}{13}\mathrm{\lambda }$

What is the ratio of wavelengths of the last line of the Balmer series and the last line of the Lyman series?

1. 1

2. 4

3. 0.5

4. 2

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is:

1. 1 : 1

2. 1 : -1

3. 2 : -1

4. 1 : -2

In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is-

1. $\frac{4}{9}$

2. $\frac{9}{4}$

3. $\frac{27}{5}$

4. $\frac{5}{27}$

The hydrogen gas with its atoms in the ground state is excited by monochromatic radiation of λ = 975 Å. The number of spectral lines in the resulting spectrum emitted will be :

1. 3

2. 2

3. 6

4. 10

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths ${\mathrm{\lambda }}_1:{\mathrm{\lambda }}_2$ emitted in the two cases is

1. 7/5

2. 20/7

3. 27/5

4. 27/20

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be 
(m is the mass of hydrogen atom, R is Rydberg constant and h is Plank’s constant)

1. $\frac{24m}{25hR}$

2. $\frac{25hR}{24m}$

3. $\frac{25m}{24hR}$

4.$\frac{24hR}{25m}$

The energy of a hydrogen atom in the ground state is -13.6eV. The energy of a He⁺ ion in the first excited state will be-

1. -13.6 eV

2. -27.2 eV

3. -54.4 eV

4. -6.8 eV