# Faint Young Sun, Radiocarbon dating

Mea Cook
,
Williams College
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#### Summary

This problem set follows lectures and readings on (1) the Stefan-Boltzmann equation and the greenhouse effect in an n-layer atmosphere and (2) radiometric dating. The goal is for the students to apply equations learned in class to real geological problems.

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## Context

#### Audience

This problem set is from a 200-level introductory undergraduate class. The students had no prerequisites except at least one semester of college-level science or math.

#### Skills and concepts that students must have mastered

The students have already calculated the black body temperature for all the planets in the solar system, and they've also calculated the optical thickness of Earth's atmosphere on the previous problem set.

#### How the activity is situated in the course

This problem set is one of the weekly problem sets given in the 12-week course.

## Goals

#### Content/concepts goals for this activity

Stefan-Boltzmann equation
greenhouse effect
albedo effect
radiocarbon dating

#### Higher order thinking skills goals for this activity

hypothesis testing

#### Other skills goals for this activity

using math to address geological questions
making simple x-y graphs

## Description of the activity/assignment

The first problem in this assignment is the culmination of the unit on energy balance and greenhouse gases. The students have already calculated blackbody temperatures as a function of albedo, sun's luminosity and distance from sun. They have also already calculated the magnitude of the greenhouse effect (optical thickness) of the modern atmosphere. In this first problem, the students apply these same calculations to the Faint Young Sun hypothesis and infer what can account for the geological evidence for liquid water on earth since 4.3 Ga. The second problem follows an introductory lecture on radiometric decay and radiometric dating. The students have seen the decay equation and learned what are decay constants and stable versus radioactive isotopes. In this problem, the students apply these concepts to radiocarbon.

## Determining whether students have met the goals

When grading this problem set, I check if the approach to the calculations was correct, and if the narrative interpretations of each step reveal that the student understood the implications of their calculations.

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