Question

The mass to charge ratio $(m/e)$ for a cation is $1.5 \times {10^{ - 8}}kg/C$. What is the mass of this atom?
A.$2.4 \times {10^{ - 19}}g$
B.$2.4 \times {10^{ - 27}}g$
C.$2.4 \times {10^{ - 14}}g$
D.None of these

Answer 1

Hint: The mass of an atom can be calculated from the mass to charge ratio as it is already given in the question that is, $m/e = 1.5 \times {10^{ - 8}}kg/C$. Where $m$ is the mass of an atom and $e$ is the magnitude of charge of an electron that is $1.602 \times {10^{ - 19}}C$ . The mass-to - charge ratio of a cation in mass spectroscopy is equivalent to the mass of the cation divided by its charge.

Complete step by step answer:
In the question it is given that;
$\dfrac{m}{e} = 1.5 \times {10^{ - 8}}kg/C$
So to calculate the mass of atom from the above formula,
$m = 1.5 \times {10^{ - 8}}kg/C \times e$
On substituting the value of charge of electron
$ = 1.5 \times {10^{ - 8}}kg/C \times 1.602 \times {10^{ - 19}}C$
$ = 2.4 \times {10^{ - 27}}kg$
But all the options are given in $g$ , not in $kg$.
So, the answer will be none of these, that is option D.


Additional information:
The mass to charge ratio is a physical quantity most generally found in charged particle electrodynamics, such as in electron optics and ion optics. It is used in electron microscopy, cathode ray tubes, accelerator physics, nuclear physics, Auger electron spectroscopy, cosmology, and mass spectrometry in research areas. Mass to charge ratio is widely used for many calculations regarding charged particles. As we stated, one of its important uses belongs to spectrometry where the mass cation comes to be an important factor.
The SI unit of mass to charge ratio is $kg/C$

Note:
The mass of the molecular ion is equal to the compound's molecular weight. Thus, the molecular ion's mass-to - charge ratio is equal to the compound's molecular weight. In spite of their very different chemical compositions, many molecules may have the same mass to charge ratio. According to classical electrodynamics, the significance of the mass to charge ratio is that, when exposed to the same electric and magnetic fields, two particles with the same mass-to - charge ratio travel along the same direction in a vacuum.