Physics quiz question: first radiation constant

Physics 205A Quiz 1, fall semester 2015
Cuesta College, San Luis Obispo, CA

The first radiation constant c₁ is given by the expression[*]:

c₁ = 2πh·c².

The Planck constant h is measured in units of kg·m²·s^–1, and the speed of light c is measured in units of m·s^–1. The units for the first radiation constant c₁ are:
(A) kg²·m⁵·s^–3.
(B) kg^1/2·m²·s^–3/2.
(C) kg·m³·s^–2.
(D) kg·m⁴·s^–3.

[*] goldbook.iupac.org/R05051.html.

Correct answer (highlight to unhide): (D)

Replacing the quantities in the equation for the first radiation constant with their kg, m and s units (while also ignoring the 2π term, as it is unitless); the units of c₁ are:

c₁ = kg·m²·s^–1·(m·s^–1)²,

c₁ = kg·m²·s^–1·m²·s^–2,

c₁ = kg·m⁴·s^–3.

Sections 70854, 70855, 73320
Exam code: quiz01rdBL
(A) : 2 students
(B) : 1 student
(C) : 15 students
(D) : 62 students

Success level: 78%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.41