Aim for FivePhysics 2

Qualitative/quantitative translation (QQT)

De Broglie wavelengths of an electron and a proton

  • Units 10 and 15
  • 8 points
  • About 18 minutes

You can use a calculator on this question, just like on exam day.

A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 15–20 minutes. This question type started in May 2025, so Physics 2 free-response questions from 2024 and earlier are built differently.

The question

An electron and a proton each start from rest and are accelerated through the same potential difference ΔV, each in the direction that increases its kinetic energy. The proton's mass is about 1840 times the electron's mass. Ignore relativistic effects.

Suggested time: 18 minutes

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Part (a)

3 points

After being accelerated, does the electron or the proton have the longer de Broglie wavelength, or are their wavelengths equal? Justify your claim. Do not use equations in this part; reason in words.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (b)

3 points

Derive an expression for the de Broglie wavelength λ of a particle of mass m and charge magnitude e accelerated from rest through potential difference ΔV. Then derive the ratio λeλp\frac{\lambda_e}{\lambda_p} of the electron's wavelength to the proton's, and evaluate it.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (c)

2 points

(i) Explain how your result from part (b) agrees with your reasoning in part (a). (ii) Predict the factor by which ΔV must be changed to make the electron's de Broglie wavelength half as long.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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