Question

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 and are masses of electron and proton respectively)

• A. $\sqrt { \frac { 1 \mathrm {~m} _ { \mathrm { e } } } { 10 \mathrm {~m} _ { \mathrm { p } } } }$
• B. $\sqrt { \frac { 1 \mathrm {~m} _ { \mathrm { p } } } { 10 \mathrm {~m} _ { \mathrm { e } } } }$
• C.
• D. $\frac { 1 \mathrm {~m} _ { \mathrm { p } } } { 10 \mathrm {~m} _ { \mathrm { e } } }$

Answer 1

Answer: (B)

$\sqrt { \frac { 1 \mathrm {~m} _ { \mathrm { p } } } { 10 \mathrm {~m} _ { \mathrm { e } } } }$

Answer 2

Kinetic energy of the electron,

……(i)

Kinetic energy of the proton,

……(ii)

Divide (i) by (ii), we get

Or $\frac { v _ { e } ^ { 2 } } { v _ { p } ^ { 2 } } = \frac { 1 } { 10 } \frac { m _ { p } } { m _ { e } }$ or $\frac { v _ { e } } { v _ { p } } = \sqrt { \frac { 1 } { 10 } \frac { m _ { p } } { m _ { e } } }$