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