Wave-Particle Duality (CIE A Level Physics)

State the formula for the de Broglie wavelength λ of a moving particle. 

State the meaning of any other symbol used. 

Electrons accelerate through a potential difference, pass through a thin crystal and are then incident on a fluorescent screen.

The pattern in Fig. 1.1 is observed on the fluorescent screen.

The potential difference used to accelerate the electron is changed.

The new pattern observed on the screen is shown in Fig. 1.2.

State and explain the change that has been made to the potential difference to create the pattern shown in Fig. 1.2.

State one piece of experimental evidence for: 

Calculate the de Broglie wavelength λ of an alpha-particle moving at a speed of 5.9 × 10⁷ m s⁻¹.

The speed v of the alpha-particles in (b)(i) is gradually reduced to zero.  

On Fig. 1.1, sketch the variation with v of λ.

Explain what is meant by the de Broglie wavelength.

A gamma-ray photon of energy 2.6 × 10⁻¹⁸ J is incident on an isolated stationary electron, as illustrated in Fig. 1.1.

 

The photon is deflected elastically by the electron through angle θ. The deflected photon has a wavelength of 590 nm.

Calculate the speed of the electron after the photon has been deflected.

Explain why the magnitude of the final momentum of the electron is not equal to the change in magnitude of the momentum of the photon.

An experiment to investigate how the de Broglie wavelength λ of an electron varies with its velocity v  is carried out. The results from this experiment are shown in Table 1.1. 

Table 1.1 

Discuss whether the data in Table 1.1 is consistent with the de Broglie equation: 

Using the data in Table 1.1 and the accepted value for Planck’s constant, comment on the accuracy of the results.

The experiment required electrons to travel at very high speeds. To achieve this, they were first accelerated through a very high voltage, V.

Show that the de Broglie wavelength λ  of these electrons is related to the accelerating voltage V  by the expression:

                     λ ∝ 

Determine the S.I. base units for h.

A researcher is investigating the de Broglie wavelength of charged particles. The charged particles are accelerated through a potential difference V.  The de Broglie wavelength λ of these particles is then determined by the researcher. Each particle has mass m and charge q.

Show that the de Broglie wavelength λ is given by the expression:

The researcher plots data points on a graph of λ² against , as shown in Fig. 1.1.

Fig. 1.1

(2)

(1)

The charge q on the particle is 2e, where e  is the elementary charge.
Use your best fit line from part (c) to show that the mass m of the particle is about 10⁻²⁶ kg.