Practicing Success

Target Exam

CUET

Subject

Physics

Chapter

Dual Nature of Radiation and Matter

Question:

If λe, λp and λα, be the de-Broglie wavelength of electron, proton and α-particle, respectively, then

Options:

λp < λα < λe 

λe < λα < λp 

λe < λp < λα   

λα < λp < λe

Correct Answer:

λα < λp < λe

Explanation:

Considering that the question indicates if the particles have same speed or K.E or accelerating potential. (Although not mentioned in question)

λ = \(\frac{h}{mv}\) or λ = \(\frac{h}{\sqrt{2m(KE)}}\) or λ = \(\frac{h}{\sqrt{2mqV}}\)

In all of the above possibilities

 λ ∝ \(\frac{1}{\sqrt{mq}}\)

And   m= 1836 me ,  mα = 4mp 

\( \sqrt{(m q)_e} < \sqrt{(m q)_p} < \sqrt{(m q)_\alpha} \)

∴ From the above relation 

λα < λp < λe