he ratio of the 'e/m' (specific charge) values of an electron and an α−particle is -

The specific charge (e/m) of a particle is calculated by dividing its charge (e) by its mass (m).

1. For an electron, the charge (e) is -1.6 x 10^-19 C and the mass (m) is 9.1 x 10^-31 kg. So, the specific charge of an electron is (-1.6 x 10^-19) / (9.1 x 10^-31) = -1.76 x 10^11 C/kg.

2. For an α-particle (which is a helium nucleus), the charge (e) is 2 x 1.6 x 10^-19 C (since it has 2 protons) and the mass (m) is 6.64 x 10^-27 kg. So, the specific charge of an α-particle is (2 x 1.6 x 10^-19) / (6.64 x 10^-27) = 4.82 x 10^7 C/kg.

3. The ratio of the specific charge of an electron to that of an α-particle is (-1.76 x 10^11) / (4.82 x 10^7) = -3657.26.

So, the ratio of the 'e/m' values of an electron and an α-particle is approximately -3657.26.