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. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass = 9.11×10^-31 kg, proton mass = 1.67×10^–27 kg, 1 eV = 1.60 ×10^–19 J).

For an electron:

Mass of the electron, m_e= 9.11×10^-31kg

Let v_e be the velocity of the electron.

Kinetic energy of the electron, K_e = m_ev_e²

⇒ 10 = m_ev_e²

⇒ m_ev_e²=20 ……………….(1)

For a proton:

Mass of the proton, m_p= 1.67×10^-27kg

Let v_p be the velocity of the proton.

Kinetic energy of the proton, K_p=m_pv_p²

⇒ 100 = m_pv_p²

⇒ m_pv_p²=200 ……………………(2)

Dividing equation (1) by (2),

⇒

⇒

⇒

⇒

⇒ = 13.54

∴ v_e:v_p = 13.54 : 1