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. $\frac{5}{27}$

Consider 3^rd orbit of He⁺ (Helium). Using non-relativistic approach, the speed of the electron in this orbit will be: (given Z = 2 and h (Planck's constant)= 6.6 x 10^-34 J-s)

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

The ratio of the longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is:

1. 3/23

2. 7/29

3. 9/31

4. 5/27

Electron in hydrogen atom first jumps from the third excited state to the second excited state and then from the 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.$\frac{24hR}{25m}$

Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited to the ground state irradiates a photosensitive material. The stopping potential is measured to be 3.57 V. The threshold frequency of the material is:

1. 4X10¹⁵ Hz

2. 5X10¹⁵ Hz

3. 1.6X10¹⁵ Hz

4. 2.5X10¹⁵ Hz

The transition from the state \(n=3\) to \(n=1\) in hydrogen-like atoms results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:
1.  $3\to 2$

2.  $4\to 2$

3.  $4\to 3$

4.  $2\to 1$