Question

The increasing order of a specific charge to mass ratio of an electron (e), proton (p), alpha particle (\[{{\alpha }}\]) and neutron (n) is:
(A) e e, p, n, \[\alpha \]
(B) n, p, e, \[\alpha \]
(C) n, \[\alpha \] , p, e
(D) n, p, \[\alpha \], e

Answer 1

Hint: The specific charge can be defined as the ratio of a charge of a subatomic particle or an ion to its mass. Now the subatomic particle under consideration could be an electro, neutron or proton. This charge to mass ratio finds to be extremely useful when we calculate the mass of any given particle. Also, it is widely used in mass spectroscopy.

Step by step solution:
To solve this question, you must know the charge and mass of an electron, proton, neutron and alpha particles.
Since a neutron is a neutral particle so it does not carry any charge that means charge on the neutron is zero. It has a mass of \[1.67 \times {10^{ - 27}}kg\].
Charge on an electron is \[1.6022 \times {10^{ - 19}}C\] and has a mass of\[9.109 \times {10^{ - 31}}kg\] .
Charge on proton is\[{{1}}{{.6022 \times 1}}{{\text{0}}^{{\text{ - 19}}}}{\text{C}}\] and has a rest of \[1.67 \times {10^{ - 27}}kg\].
Charge of an alpha particle is two times that of a proton and has a mass of 4 times that of proton.
Now, we calculate the ratio of specific charge to its mass.
Since charge on a neutron is zero so its ratio is also zero.
For electron, \[\dfrac{e}{m} = \dfrac{{1.6022 \times {{10}^{ - 19}}C}}{{9.109 \times {{10}^{ - 31}}kg}} = 1.76 \times {10^{11}}C/kg\]
For proton, \[\dfrac{e}{m} = \dfrac{{1.6022 \times {{10}^{ - 19}}C}}{{1.67 \times {{10}^{ - 27}}kg}} = 9.58 \times {10^7}C/kg\]
For alpha particle, \[\dfrac{e}{m} = \dfrac{{2 \times 1.6022 \times {{10}^{ - 19}}C}}{{4 \times 1.67 \times {{10}^{ - 27}}kg}} = 4.8 \times {10^7}C/kg\]
So, the increasing order of specific charge is n < \[{{\alpha }}\]< p < e.

Hence the correct option is C.

Note: The different elementary particles are often simply differentiated on the basis of two major criteria: Mass and Charge. Neutrons are neutral particles present inside the nucleus of an atom. Protons are positively charged particles also present inside the nucleus. Electrons are negatively charged particles revolving around the nucleus of an atom.