---
title: Homework 1
allDay: false
startTime: 11:30
endTime: 15:30
date: 2024-09-03
completed: null
type: single
---
# Preamble
Dane Sabo
Dane.Sabo@pitt.edu
September 3rd, 2024
# Instructions
Complete the problems below being sure to show your work. If you need to lookup nuclear data from an external source please reference the source in your solutions.
# Problems
**1. How many neutrons and protons are there in the nuclei of the following atoms:**

| Atom              | Protons | Neutrons |
| ----------------- | ------- | -------- |
| $^7\text{Li}$     | 3       | 4        |
| $^{24} \text{Mg}$ | 12      | 12       |
| $^{135}\text{Xe}$ | 54      | 81       |
| $^{209}\text{Bi}$ | 83      | 126      |
| $^{222}\text{Rn}$ | 86      | 136      |
**2. The atomic weight of $^{59}\text{Co}$ is 58.93319. How many times heavier is $^{12}\text{C}$? **
$\frac{ ^{59}\text{Co}}{^{12}\text{C}} = \frac{58.93319}{12.00000} = 4.91110 \text{ times larger}$

**3. How many atoms are there in 10g of $^{12}\text{C}$?**
$10 \text{g} \times \frac{1 \text{ mol } ^{12}\text{C}}{12 \text{g}} \times \frac{0.6022045 \times 10^{24} \text{ atoms}}{1 \text{ mol } ^{12}\text{C}} = 5.0184 \times 10^{23} \text{ atoms of } ^{12} \text{C}$
**4. A beaker contains 50 g of ordinary water.**
	*a. How many moles of water are present?*
	$50 \text{g} \times \frac{1 \text{ mol } H_2O}{18.01528 \text{g}} = 2.77542 \text{ moles of water}$
	*b. How many hydrogen atoms?*
	$2.77542 \text{ moles of water } \times \frac{2 \text{mol} H}{1 \text{mol} H_2O} \times \frac{0.6022045 \times 10^{24} \text{ atoms}}{1 \text{ mol }}$
	
	*c. How many deuterium atoms?*
**5. Find the mass of an atom of $^{235}\text{U}$**
	*a. in amu;*
	*b. in grams.*
**6. The complete combustion of 1 kg of bituminous coal releases about $3\times 10^7 \text{J}$ in heat energy. The conversion of 1 g of mass into energy is equivalent to the burning of how much coal?**
**7. Tritium ($^3\text{H}$) decays by negative beta decay with a half-life of 12.26 years. The atomic weight of $^3\text{H}$ is 3.016.**
	*a. To what nucleus does $^3\text{H}$ decay?*
	*b. What is the mass in grams of 1 mCi of tritium?*
**8. Approximately what mass of $^{90}\text{Sr}$ (T-1/2 = 28.8 years) has the same activity as 1g of $^{60}\text{Co}$ (T-1/2 = 5.26 years)?**
**9. Using the chart of the nuclides, complete the following reactions. If a daughter nucleus is radioactive, indicate the complete decay chain:**