Physics quiz question: inverse Rydberg constant

Physics 205A Quiz 1, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 1.85

Three physical constants are:

      Rydberg unit of energy, Ry = 2.2×10^–18 kg·m²·s^–2.
      The speed of light, c = 3.0×10⁸ m·s^–1.
      Planck's constant, h = 6.6×10^–34 kg·m²·s^–1.

Which combination of these three constants results in dimensions of length?
(A) Ry^–1 × c^–1 × h^–1.
(B) Ry^–1 × c × h.
(C) Ry × c^–1 × h.
(D) Ry × c × h^–1.

Correct answer: (B)

Only the Rydberg unit of energy Ry and Planck's constant h have units of kg, and so must cancel each other out. This eliminates response (A) and (C), leaving (B) and (D) as possible remaining correct choices. The units of s must also cancel out, such that the speed of light c and Planck's constant h must both cancel out the Rydberg unit of energy Ry. This eliminates response (D), leaving (B) as the correct answer.

To verify that the units will properly work out for response (B):

Ry^–1 × c × h = (kg·m²·s^–2)^-1 × (m·s^–1) × (kg·m²·s^–1),

= kg^-1·m^-2·s² × m·s^–1 × kg·m²·s^–1,

= kg^-1·m^-2·s² × m·s^–1 × kg·m²·s^–1,

= m^-2 × m × m²,

= m^-2 × m × m²,

= m.

Student responses
Sections 70854, 70855
Exam code: quiz01bL0t
(A) : 4 students
(B) : 32 students
(C) : 10 students
(D) : 15 students

Success level: 52% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.87