The de-Broglie wavelength of an electron in the first Bohr orbit is

• equal to half the circumference of the first orbit

• equal to one fourth the circumference of the first orbit

• equal to the circumference of the first orbit

• equal to twice the circumference of the first orbit

Whenever a hydrogen atom emits a photon in the Balmer series, it

• may emit another photon in the Paschen series

• need not emit any more photon

• may emit another photon in the Balmer series

• must emit another photon in the Lyman series

In the Bohr model of the hydrogen atom, let R, V and E represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantity is proportional to the quantum number n ?

• $\frac{\mathrm{E}}{\mathrm{V}}$

• $\frac{\mathrm{R}}{\mathrm{E}}$

• VR

• RE

Given the value of rydberg constant is 10 m^-1, the wave number of the last line of the Balmer series in hydrogen spectrum will be:

• 0.5 x 10⁷ m^-1

• 0.25 x 10⁷ m^-1

• 2.5 x10⁷ m^-1

• 2.5 x10⁷ m^-1

The ratio of escape velocity at earth (V_e) to the escape velocity at a planet (v_p) whose radius and mean density are twice as that of earth is,

• 1:

• 1:4

• 1:

• 1:

Consider 3^rd orbit of He⁺ (Helium)_, using non-relativistic approach, the speed of electron in this orbit will be (given K= 9 x 10⁹ constant, Z=2 and h (Planck's constant = 6.6 x 10^-34 Js^-1

• 2.92 x 10⁶ m/s

• 1.46 x 10⁶ m/s

• 0.73 x 10⁶ m/s

• 0.73 x 10⁶ m/s

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in the uniform magnetic field. What should be the energy of an alpha particle to describe a circle of the same radius in the same field.

• 2 MeV

• 1 MeV

• 0.5 MeV

• 0.5 MeV

The transition from the state n = 3 to n=1 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from.

• 2→ 1 

• 3 →2

• 4 → 2

• 4 → 2

An 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 λ₁:λ₂ emitted in the two cases is

• 7/5

• 27/20

• 27/5

• 27/5

An electron of a stationary hydrogen atom passes from the fifth energy level to ground level. The velocity that the atom acquired as a result of photon emission will be