Physics quiz question: fine structure constant units

Physics 205A Quiz 1, fall semester 2016
Cuesta College, San Luis Obispo, CA

The Rydberg constant R (measured in units of m–1) is a physical constant used in spectroscopy[*]:

R = α2·me·c/(2·h).

The electron mass me is measured in units of kg, the speed of light c is measured in units of m·s–1, and the Planck constant h is measured in units of kg·m2·s–1. The units for the constant α are:
(A) kg1/2·m3/2.
(B) m2·s–1.
(C) kg·m·s.
(D) (No units, as it is a dimensionless quantity.)

[*] wki.pe/Rydberg_constant#Alternative_expressions.

Correct answer (highlight to unhide): (D)

The constant α can be expressed as:

α = sqrt(2·h·R/(me·c)),

and replacing the quantities in the equation with their kg, m and s units, the units of α are:

α = sqrt((kg·m2·s–1)·(m–1)/((kg)·(m·s–1))),

α = sqrt((kg·m·s–1)/(kg·m·s–1)),

α = sqrt(1);

thus making α a dimensionless quantity.

Sections 70854, 70855, 73320
Exam code: quiz01bIR6
(A) : 11 students
(B) : 14 students
(C) : 6 students
(D) : 26 students

Success level: 46%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50

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