Question

Which of the following is correctly matched?
a.) The momentum of H-atom when electrons return from ${ n = 2 }$ to ${ n = 1 }$: $\dfrac{3Rh}{4}$
b.) The momentum of a photon: Independent of a wavelength of light
c.) e/m ratio of anode rays: Independent of gas in the discharge tube
d.) The radius of the nucleus: ${{(mass\ number)}^{1/2}}$

Answer 1

It is important to understand the terms momentum, wavelength and e/m ratio in the view of a hydrogen atom. Scientist Neils Bohr gave a concise idea about the working of subatomic particles and how the terms momentum, radius and wavelength are interrelated. Based on the Rydberg formula, you can possibly arrive at the correct answer.

Complete step by step answer:
As we know, momentum = $\dfrac{h}{\lambda }=h\left[ R(\dfrac{1}{{{1}^{2}}}-\dfrac{1}{{{2}^{2}}} \right]=\dfrac{3Rh}{4}$
where h = Planck’s constant
= De Broglie wavelength of light
R = Rydberg constant
Hence, The momentum of H-atom when electrons return from ${ n = 2 }$ to ${ n = 1 }$ is equal to $\dfrac{3Rh}{4}$
As we know,
$\lambda =\dfrac{h}{p}$
From here, we see that the momentum of a photon is inversely proportional to the wavelength of light.
Hence, the momentum of a photon: Independent of a wavelength of light is incorrect.
The e/m ratio depends on the gas in the discharge tube, so the statement “e/m ratio of anode rays: Independent of gas in the discharge tube” is incorrect.
The radius of the nucleus is directly proportional to ${{(mass\ number)}^{1/3}}$.
Hence, this statement is incorrect.
So, the correct answer is “Option A”.

Note: The possibility to make a mistake is that you may choose option B. The momentum is dependent on the wavelength of light not independent of a wavelength of light.