Question

Find the ratio of specific charges ($\dfrac{q}{m}$ ) of an $\alpha$-particle and a deuteron.

Answer 1

$\dfrac{q}{m}$ ratio is a charge to mass ratio. $\alpha$ particle, deuteron, electron, proton and neutron all are subatomic particles that were discovered during the twentieth century.

Complete step by step answer:
Charge to the mass ratio was measured for electrons by J.J Thomson, a british physicist using cathode ray tube and applying magnetic and electric fields perpendicular to each other as well as to the path of the electrons.
He made certain arguments which are, the magnitude of the negative charge on the particle, greater the magnitude of the charge on the particle and more will be the deflection due to greater interaction. Also lesser the mass of the particle more will be the deflection.
Now to calculate specific charge for $\alpha$-particle and deuteron, let us analyse their mass and charge. $\alpha$-particle also called as helium is a positively charged particle consisting of two protons and deuterons having a charge +2 and mass 4 amu whereas deuteron has a mass 2 amu which is why it is also called two hydrogen and has a charge +1e.
Now let us find the charge to mass ratio for both the particles, therefore we get
${\left( {\dfrac{q}{m}} \right)_\alpha } = \dfrac{{2e}}{{4m}} \\\ \Rightarrow {\left( {\dfrac{q}{m}} \right)_{deuteron}} = \dfrac{e}{{2m}}$
Further we are asked to find the ratio of the specific charge of helium to deuteron which will be,
Ratio=$\dfrac{e}{{2m}} \times \dfrac{{4m}}{{2e}} = 1:1$

Hence the ratio of specific charges is 1:1 for helium and deuteron.

Note: The charge to the mass ratio of the particles is found to depend on the gas from which these originate. Some of the positively charged particles carry a multiple of the fundamental unit of electrical charge.