Question

Find the ratio of the final speed of the electron to the final speed of the hydrogen ion, assuming non-relativistic speeds. Take the mass of the hydrogen ion to be equal to the proton mass, 1.67 × 10–27 kg.

Answer 1

`(V_(e))/(V_(h))=0.428*10^(2)`

Step-by-step explanation:

From conservation of energy states that

`K_(i)+v_(i)=v_(f)+K_(f)\\ as\\K_(i)=0\\K_(f)=1/2mv^(2)\\ v_(i)=qv\\v_(f)=0\\So\\qv=1/2mv^(2)\\ v=\sqrt{(2qv)/(m) }\\ Velocity_(electron)=\sqrt{(2qv)/(m_(e)) }\\Velocity_(hydrogen)=\sqrt{(2qv)/(m_(h)) }\\(V_(e))/(V_(h))=\sqrt{((2qv)/(m_(e)))/((2qv)/(m_(h)))}\\(V_(e))/(V_(h))=\sqrt{(m_(h))/(m_(e)) }\\(V_(e))/(V_(h))=\sqrt{(1.67*10^(-27) )/(9.11*10^(-31) ) }\\(V_(e))/(V_(h))=0.428*10^(2)`