Unit 2 — Introduction to Modern Physics · Physics. These are 10 questions from the Magmo3 bank on this lesson, from easy to hard. Solve each one, then open "Show answer and explanation". Magmo3 has 63 questions on this lesson, each with an explanation.
According to de Broglie's hypothesis, wave–particle duality is a property of…
Correct answer: (C) all moving material particles
Explanation: de Broglie proposed that every moving material particle has an associated wavelength, so duality applies to all of them.
For a particle of mass (m) moving with speed (v), the de Broglie wavelength is expressed as…
Correct answer: (D) λ = h/(mv)
Explanation: Substituting the momentum p = mv into λ = h/p gives λ = h/(mv).
When an electron is accelerated from rest through a potential difference (V), the kinetic energy it gains is equal to…
Correct answer: (D) the product of its charge and the potential difference (eV)
Explanation: The work done on the electron equals its charge times the accelerating potential difference, giving KE = eV.
A particle moves with a momentum of 3.3 × 10⁻²⁴ kg·m/s. Using h = 6.6 × 10⁻³⁴ J·s, the de Broglie wavelength associated with its motion equals…
Correct answer: (C) 2.0 × 10⁻¹⁰ m
Explanation: λ = h/p = (6.6 × 10⁻³⁴)/(3.3 × 10⁻²⁴) = 2.0 × 10⁻¹⁰ m.
Two electrons X and Y have momenta in the ratio pX : pY = 1 : 4. The ratio between their de Broglie wavelengths λX : λY equals…
Correct answer: (C) 4 : 1
Explanation: Because λ is inversely proportional to p, λX : λY = pY : pX = 4 : 1.
An electron of mass 9.1 × 10⁻³¹ kg has a de Broglie wavelength of 7.3 × 10⁻¹⁰ m. Using h = 6.6 × 10⁻³⁴ J·s, its speed is approximately…
Correct answer: (C) 1.0 × 10⁶ m/s
Explanation: v = h/(mλ) = (6.6 × 10⁻³⁴)/(9.1 × 10⁻³¹ × 7.3 × 10⁻¹⁰) ≈ 1.0 × 10⁶ m/s.
In an electron microscope, the electron beam has a de Broglie wavelength λ when accelerated through a potential difference V. To reduce the wavelength to λ/3, the accelerating potential difference must be changed to…
Correct answer: (C) 9V
Explanation: Since λ ∝ 1/√V, reducing λ by a factor of 3 requires increasing V by a factor of 9.
Three particles move as follows: an electron of speed 2v, a proton of speed v, and an alpha particle of speed v (mass of the alpha particle = 4 × mass of the proton ≫ mass of the electron). Arrange the particles in order of increasing de Broglie wavelength.
Correct answer: (B) λ_α < λ_proton < λ_electron
Explanation: λ = h/(mv); the momenta rank alpha (4mₚ·v) > proton (mₚ·v) > electron (2mₑ·v), so the wavelengths rank oppositely: λ_α < λ_proton < λ_electron.
An electron is accelerated from rest through a potential difference of 100 V. Using h = 6.6 × 10⁻³⁴ J·s, mₑ = 9.1 × 10⁻³¹ kg and e = 1.6 × 10⁻¹⁹ C, the de Broglie wavelength of the electron is approximately…
Correct answer: (C) 1.2 × 10⁻¹⁰ m
Explanation: p = √(2meV) = 5.4 × 10⁻²⁴ kg·m/s, so λ = h/p ≈ 1.2 × 10⁻¹⁰ m.
An X-ray photon of wavelength 2.00 × 10⁻¹¹ m is scattered by a free electron through 180°. Given that the maximum Compton shift is 4.85 × 10⁻¹² m, the wavelength of the scattered photon is...
Correct answer: (B) 2.49 × 10⁻¹¹ m
Explanation: λ' = λ + Δλ = 2.00×10⁻¹¹ + 0.485×10⁻¹¹ = 2.49 × 10⁻¹¹ m.
The first 10 questions in every subject are free, each with an explanation.