A proton and an α-particle are accelerated from rest to the same energy. The de-Broglie wavelengths λ_p and λ_α are in the ratio
NEET UG 2019 — Physics Modern Physics
2019mcqeasy
A proton and an α-particle are accelerated from rest to the same energy. The de-Broglie wavelengths λp and λα are in the ratio
Official previous-year question
Held on 30 Apr 2019 · Verified 9 Jul 2026.
Options
A
2:1
B
1:1
C
2:1
D
4:1
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Solution
The de-Broglie wavelength associated with a charged particle is given by λ=ph where, h= planck's constant and p= momentum =2mKE (here, KE is the kinetic energy of the charged particle) ⇒λ=2mKEh For proton and α-particle, the wavelengths are respectively given as, λp=2mpKEph and λα=2mαKEαh∴λαλp=2mpKEP2mαKEα Here, KEα=KEp and mα=4mp Substituting these above mentioned relations in Eq. (i), we get ⇒λαλP=mp4mP=12 or λP:λα=2:1
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