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An electron and a proton are detected in...

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. The ratio of their speeds is
(where `m_e` and `m_p` are masses of electron and proton respectively)

A

`sqrt(1/10 m_e/m_p)`

B

`sqrt(1/10 m_p/m_e)`

C

`1/10 m_e/m_p`

D

`1/10 m_p/m_e`

Text Solution

Verified by Experts

The correct Answer is:
B
Kinetic energy of the electron,
`K_e=1/2m_ev_e^2=10 eV` ...(i)
Kinetic energy of the proton,
`K_p=1/2m_p v_p^2=100eV`…(ii)
Divide (i) by (ii), we get
`(m_ev_e^2)/(m_pv_p^2)=1/10 " " "or"v_e^2/v_p^2=1/10m_p/m_e " " or " " v_e/v_p=sqrt(1/10m_p/m_e)`
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