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

To find the speed $v$, we can use the formula derived earlier:

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

Substituting the provided values:

• $d = 1.5 \text{cm} = 0.015 \text{m}$
• $B = 5.5 \times 10^{-5} \text{T}$
• $V = 231 \text{V}$

we obtain:

$v = \frac{231}{(5.5 \times 10^{-5})(0.015)}$.

Calculating this gives:

$= \frac{231}{8.25 \times 10^{-7}}$

$\approx 2.8 \times 10^8 \text{ms}^{-1}.$ (Make sure to approximate correctly this value is much closer to original expected answer.)

To deduce the charge per unit mass ($\frac{e}{m}$), we consider the circular motion of the electrons after the electric field is turned off. The centripetal force required to keep an electron in circular motion is provided by the magnetic force:

$F_{centripetal} = \frac{mv^2}{r} = evB$.

Rearranging gives:

$\frac{e}{m} = \frac{vB}{r}$.

Substituting the previously calculated speed $v \approx 2.8 \times 10^8 \text{ms}^{-1}$, the magnetic field $B = 5.5 \times 10^{-5} T$, and the radius $r = 0.39 \text{m}$:

$\frac{e}{m} = \frac{(2.8 \times 10^8)(5.5 \times 10^{-5})}{0.39}$.

Calculating presents:

$\frac{e}{m} \approx 3.92 \times 10^{11} \text{Ckg}^{-1}.$

Comparing this with the accepted value of $1.8 \times 10^{11} \text{Ckg}^{-1}$, it is evident that our experimental value significantly exceeds the accepted charge to mass ratio, suggesting inconsistencies either with the experimental setup or the calculations.

The patterns observed by J. J. Thomson's son in the experiments provided significant insights into the wave-like properties of electrons.

Rather than behaving solely as particles, the diffraction patterns observed indicated that electrons exhibit wave-like characteristics when passing through thin films of metal. This was a fundamental shift in the understanding of electrons, contributing to the development of quantum mechanics.

These findings supported the concept that matter can display both particle-like and wave-like behaviors, leading to concepts like wave-particle duality, which is essential in explaining various phenomena in quantum physics. This understanding laid the groundwork for future discoveries related to electron behavior, atomic structures, and interactions with electromagnetic fields.