Question

What is the increasing order for the value of e/m (charge to mass ratio) for electron (e), proton (p), neutron (n) and alpha particle ($\alpha $)?
\[
  {\text{A}}{\text{. e}} < {\text{p}} < {\text{n}} < \alpha \\
  {\text{A}}{\text{. n}} < {\text{p}} < {\text{e}} < \alpha \\
  {\text{C}}{\text{. n}} < {\text{p}} < \alpha < {\text{e}} \\
  {\text{D}}{\text{. n}} < \alpha < {\text{p}} < {\text{e}} \\
 \]

Answer 1

Hint: Here, we will proceed by simply discussing the subatomic particles electron, proton, neutron and alpha particle. We will also write down the masses and charges corresponding to these particles and then find the charge to mass ratio for all.

Complete step by step answer:
Electron is basically the lightest stable subatomic particle and is represented by letter e. An electron is a negatively charged particle with a charge magnitude of $1.6 \times {10^{ - 19}}$ Coulomb (C). Also, the rest mass of the electron is $9.11 \times {10^{ - 31}}$ kg.

So, the charge to mass ratio for electron will be given as
${\left( {\dfrac{{{\text{Charge}}}}{{{\text{Mass}}}}} \right)_{\text{e}}} = \dfrac{{1.6 \times {{10}^{ - 19}}}}{{9.11 \times {{10}^{ - 31}}}} = 0.176 \times {10^{12}} = 1760 \times {10^8}$ C/kg
Proton is another stable subatomic particle and is represented by letter p. A proton is a positively charged particle having charge equal in magnitude as that of an electron i.e., $1.6 \times {10^{ - 19}}$
Coulomb (C). Also, the mass of the proton is $1.67 \times {10^{ - 27}}$ kg.

So, the charge to mass ratio for proton will be given as
${\left( {\dfrac{{{\text{Charge}}}}{{{\text{Mass}}}}} \right)_{\text{p}}} = \dfrac{{1.6 \times {{10}^{ - 19}}}}{{1.67 \times {{10}^{ - 27}}}} = 0.958 \times {10^8}$ C/kg

Neutrons are also stable subatomic particles and are represented by letter n. A neutron is a neutral particle having no charge i.e., Charge of neutron = 0. Also, the mass of the neutron is the same as that of proton i.e., $1.67 \times {10^{ - 27}}$ kg.

So, the charge to mass ratio for neutron will be given as
${\left( {\dfrac{{{\text{Charge}}}}{{{\text{Mass}}}}} \right)_{\text{n}}} = \dfrac{0}{{1.67 \times {{10}^{ - 27}}}} = 0$ C/kg

Alpha particle is basically a positively charged particle which is identical to the nucleus of a helium atom (He). This particle is denoted by $\alpha $. Any alpha particle can be represented as ${\text{H}}{{\text{e}}^{2 + }}$. Clearly, charge of alpha particle is twice that of the electron (i.e., 2e = $2 \times 1.6 \times {10^{ - 19}} = 3.2 \times {10^{ - 19}}$ C) and mass of alpha particle is $6.65 \times {10^{ - 27}}$ kg.

So, the charge to mass ratio for alpha particle will be given as
${\left( {\dfrac{{{\text{Charge}}}}{{{\text{Mass}}}}} \right)_{\text{alpha }}} = \dfrac{{3.2 \times {{10}^{ - 19}}}}{{6.65 \times {{10}^{ - 27}}}} = 0.48 \times {10^8}$ C/kg
Therefore, the increasing order of the value of e/m (charge to mass ratio) for electron (e), proton (p), neutron (n) and alpha particle ($\alpha $) is n<$\alpha $
So, the correct answer is “Option D”.

Note: If we will carefully see, we will analyse that the mass of the electron is very less as compared to the masses of proton and neutron i.e., mass of the proton is nearly 1836 times the rest mass of the electron. That’s why while calculating the mass number of an atom, the mass of the electron is not counted.