Question

The ratio of ${\text{e/m}}$ for a cathode ray:
A) Varies with a gas discharge tube.
B) Is fixed.
C) Varies with different electrodes.
D) Is maximum if hydrogen is taken.

Answer 1

Hint: We know that cathode rays are made up of negatively charged particles i.e. electrons. When cathode rays travel through any gases they ionize the gases. The ratio of ${\text{e/m}}$ for a cathode ray is the ratio of the charge of the particle in coulombs to the mass of the particle of cathode ray in kilograms.

Complete step-by-step answer:
We know that cathode rays are made up of negatively charged particles i.e. electrons. When cathode rays travel through any gases they ionize the gases. The ratio of ${\text{e/m}}$ for a cathode ray is the ratio of the charge of the particle in coulombs to the mass of the particle of cathode ray in kilograms.

We know that cathode rays consist of an electron. The charge on electron is $1.6 \times {10^{ - 19}}{\text{ C}}$ and the mass of electron is $9.1 \times {10^{ - 31}}{\text{ kg}}$. Thus, the ratio of ${\text{e/m}}$ for a cathode ray is,
$\dfrac{{\text{e}}}{{\text{m}}} = \dfrac{{1.6 \times {{10}^{ - 19}}{\text{ C}}}}{{9.1 \times {{10}^{ - 31}}{\text{ kg}}}} = 1.758820 \times {10^{11}}{\text{ C/kg}}$

Thus, the ratio of ${\text{e/m}}$ for a cathode ray is $1.758820 \times {10^{11}}{\text{ C/kg}}$.
The ratio of ${\text{e/m}}$ for a cathode ray does not depend on the gas filled in the discharge tube. The constituent particle for cathode ray remains the same i.e. electron. And thus the ratio of ${\text{e/m}}$ remains constant or fixed. Thus, the ratio of ${\text{e/m}}$ for a cathode ray is fixed.

Thus, the correct answer is option (B) is fixed.

Note: The cathode rays consist of electrons. These electrons are moving with high speed and all these electrons are identical. Thus, the charge by mass ratio of cathode rays is the same for all the gases. For positively charged ions the charge by mass ratio changes as the number of nucleons changes.