Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous \(\alpha\)-decay with sam…

For \(\alpha\)-decay, kinetic energy of the \(\alpha\)-particle is

\({K}_{\alpha }=\left(\frac{A-4}{A}\right)Q\)

For substance A with mass number 200:

\({K}_{\alpha 1}=\frac{196}{200}Q\)

For substance B with mass number 212:

\({K}_{\alpha 2}=\frac{208}{212}Q\)

Therefore,

\(\frac{{K}_{\alpha 1}}{{K}_{\alpha 2}}=\frac{196}{200}\cdot \frac{212}{208}=\frac{2597}{2600}\)