Verified Solution • 2025–26 Session moderate

QJEEM23Ph74fc: JEE Main 2023 Physics - Class 12 JEEM23Ph74fc Solution: A proton moving with one tenth of velocity of light has a…

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ\lambda . An alpha particle having certain kinetic energy has the same de-Brogle wavelength λ\lambda . The ratio of kinetic energy of proton and that of alpha particle is:

Multiple Choice Options

  • A 1:04
  • B 2:01
  • C 4:01
  • D 1:02

Step-by-Step Verified Solution

For same λ1\lambda_{1} momentum should be same,

(P)P=(P)α(P)_{P}=(P)_{\alpha}

⇒2kPmP=2kαmα\Rightarrow \sqrt{2 k_{P} m_{P}}=\sqrt{2 k_{\alpha} m_{\alpha}}

⇒kPmP=kαmα\Rightarrow k_{P} m_{P}=k_{\alpha} m_{\alpha}

⇒kPkα=(mαmP)=41=4:1\Rightarrow \frac{k_{P}}{k_{\alpha}}=\left(\frac{m_{\alpha}}{m_{P}}\right)=\frac{4}{1}=4: 1

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