17 (a) In 1897 J J Thomson demonstrated that electrons are small negative particles - Edexcel - A-Level Physics - Question 17 - 2023 - Paper 4

Given:

• d = 1.5 cm = 0.015 m
• B = 5.5 × 10^-5 T
• V = 231 V

We can now calculate the speed v using the derived formula:

$v = \frac{V}{Bd}$

Substituting the values:

$v = \frac{231 \text{ V}}{(5.5 \times 10^{-5} \text{ T})(0.015 \text{ m})}$

Calculating the denominator:

$Bd = 5.5 \times 10^{-5} \times 0.015 = 8.25 \times 10^{-7}$

Now calculating v:

$v = \frac{231}{8.25 \times 10^{-7}}\approx 2.8 \times 10^{8} \text{ ms}^{-1}$

Therefore, we find that v is approximately equal to 3 × 10^7 ms^-1.

Using the radius of the circular path of the electron:

• r = 39 cm = 0.39 m

The centripetal force required for the circular motion is provided by the magnetic force:

$\frac{mv^2}{r} = evB$

From this, we can express the charge-to-mass ratio (e/m) as:

$\frac{e}{m} = \frac{v}{rB}$

Substituting our known values: $v \approx 3 \times 10^{7}\text{ ms}^{-1}, \ r = 0.39 \text{ m}, \ B = 5.5 \times 10^{-5} \text{ T}$

Now calculating:

$\frac{e}{m} = \frac{3 \times 10^{7}}{0.39 \times 5.5 \times 10^{-5}}\approx 2.0 \times 10^{11} C/kg$

The accepted value is 1.8 × 10^{11} C/kg, which is consistent with our calculation.

J.J. Thomson's experiments demonstrated that electrons are not just particles, but exhibit wave-like behavior as well.

The observed patterns from the electron beams interacting with thin metal films indicated interference patterns, similar to those produced by light waves. This led to the understanding that electrons can behave as waves, a concept pivotal to quantum mechanics, establishing the dual nature of electrons.

Prior to this, electrons were primarily viewed as particles; however, this experiment prompted scientists to reconsider electron behavior, contributing to the development of quantum theory and the modern understanding of atomic and subatomic structures.