2019 A/L Physics Past Paper · Question 12 (English Medium)

X-ray production: the incorrect statement

Which of the following statements regarding the X-ray production in common applications is incorrect?

(1) Two circuits are used in the X-ray production system.
(2) Anode could be damaged due to the bombardment of electrons.
(3) Low voltage is sufficient to heat the cathode.
(4) Energy of the X-rays emitted depends on the current through the filament.
(5) X-ray tube must be evacuated to avoid the energy loss of electrons.

Answer and explanation

Answer: (4) Energy of the X-rays emitted depends on the current through the filament.

What the question asks

We want:

Which of the five statements about the X-ray tube is not correct.

The five statements are about the circuits, the anode, the voltage for the filament, what decides the X-ray energy, and the air in the tube.

Relevant theory

The other producers of E.M. waves are ‘X-ray tubes’, ‘Magnetrons’.

Gases get ionized when X-rays are travelling through them.

A small voltage heats the filament, the cathode.

The hot filament frees electrons.

A high voltage $V$ pulls the electrons to the anode.

Each electron gains the energy $eV$ .

When it stops in the anode, a part of its energy leaves as an X-ray.

So the greatest X-ray energy is:

$E_{max} = eV$

It depends on $V$ only.

The filament current only changes how many electrons are freed. So it changes how many X-rays come out.

On that occasion, if the frequency of an X-ray photon is f, then the kinetic energy in the electron reaching the target can be given as K = eV.

Reading the options

Each statement is compared with how the tube works.

(1) Two circuits

Correct

One circuit for the filament and one for the electrons

(2) The anode can be damaged

Most of the electron energy turns into heat

(3) A low voltage heats the filament

A few volts are enough to heat the filament

(4) X-ray energy depends on the filament current

Incorrect

The energy is $eV$ . The current only changes how many X-rays come out

(5) The tube has no air

Air would make the electrons lose energy

$40$

$E = eV = 40\ \text{keV}$

$80$

$E = eV = 80\ \text{keV}$

Now compare with the options.

Statements 1, 2, 3 and 5 are correct.

Only statement 4 is not.

Doubling the filament current leaves the energy at 40 keV.

Only doubling the voltage doubles it.

Why the other options fail

This statement is correct. There are two circuits.

This statement is correct. The heat can damage the anode.

This statement is correct. A low voltage is enough for the filament.

This statement is correct. The tube has no air.

Conclusion

$E_{max} = eV$

The X-ray energy is $eV$ .

It depends on the voltage, not on the filament current.

So the statement that is not correct is (4).

Thinking that a bigger filament current gives X-rays with more energy.

A bigger filament current gives more X-rays. The energy of each X-ray is set by the voltage.

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