Question

1. state the number of neutrons and protons in each of the following nuclei.

a.
b.
c.
d.

1. the three types of radioactive emissions are called alpha (α), beta (β) and gamma (γ) radiation. complete the table below with the correct information about each type:

	charge	atomic symbol	can be stopped by
beta
gamma

1. which of the three radioactive emissions (α, β, γ) best fit the following statements? write the correct symbols on the lines.

a) these emissions are charged.
b) this emission is the most massive (heaviest).
c) this emission is the most charged.
d) this emission is most dangerous outside of the body.
e) this emission is stopped by thin paper or a few centimeters of air.
f) this emission can travel through paper, but is stopped by aluminum.
g) this emission can travel through fairly thick lead.

1. which type of radiation - alpha, beta, or gamma?

a. results in the greatest change in atomic number? why?

b. results in the least change in atomic number? why?

Explanation:

Step 1: Recall Atomic Structure Basics

For an atom represented as \( _Z^A X \), \( Z \) is the atomic number (number of protons), and the number of neutrons \( N = A - Z \), where \( A \) is the mass number.

Step 1a: Analyze \( _1^3 H \)

• Atomic number \( Z = 1 \) (protons = 1).
• Mass number \( A = 3 \).
• Neutrons \( = A - Z = 3 - 1 = 2 \).

Step 1b: Analyze \( _6^{12} C \)

• Atomic number \( Z = 6 \) (protons = 6).
• Mass number \( A = 12 \).
• Neutrons \( = 12 - 6 = 6 \).

Step 1c: Analyze \( _{26}^{56} Fe \)

• Atomic number \( Z = 26 \) (protons = 26).
• Mass number \( A = 56 \).
• Neutrons \( = 56 - 26 = 30 \).

Step 1d: Analyze \( _{82}^{207} Pb \)

• Atomic number \( Z = 82 \) (protons = 82).
• Mass number \( A = 207 \).
• Neutrons \( = 207 - 82 = 125 \).

Step 2: Recall Properties of Radioactive Emissions

Emission	Charge	Atomic Symbol	Stopped By
Beta (\( \beta \))	\( -1 \)	\( _{-1}^0 e \)	Aluminum foil
Gamma (\( \gamma \))	\( 0 \)	\( \gamma \)	Thick lead, concrete

Step 3: Match Emissions to Statements

a) Charged emissions: \( \alpha \) (\( +2 \)) and \( \beta \) (\( -1 \)) (gamma is neutral).
b) Most massive: \( \alpha \) (mass ~4 amu, beta ~1/1836 amu, gamma massless).
c) Most charged: \( \alpha \) (charge \( +2 \), beta \( -1 \), gamma \( 0 \)).
d) Most dangerous outside body: \( \gamma \) (penetrates deeply; alpha/beta are less penetrating outside).
e) Stopped by thin paper: \( \alpha \).
f) Travels through paper, stopped by aluminum: \( \beta \).
g) Travels through thick lead: \( \gamma \) (needs thick lead/concrete).

Step 4: Analyze Atomic Number Change

• Alpha decay: \( _Z^A X

ightarrow _{Z-2}^{A-4} Y + _2^4 He \) → Atomic number decreases by 2.

• Beta decay: \( _Z^A X

ightarrow _{Z+1}^A Y + _{-1}^0 e \) → Atomic number increases by 1.

• Gamma decay: \( _Z^A X^*

ightarrow _Z^A X + \gamma \) → No atomic number change.

a) Greatest change: Alpha (changes \( Z \) by 2).
b) Least change: Gamma (no change in \( Z \)).

Answer:

1. Number of Neutrons and Protons

a. \( _1^3 H \): Protons = 1, Neutrons = \( 3 - 1 = 2 \)
b. \( _6^{12} C \): Protons = 6, Neutrons = \( 12 - 6 = 6 \)
c. \( _{26}^{56} Fe \): Protons = 26, Neutrons = \( 56 - 26 = 30 \)
d. \( _{82}^{207} Pb \): Protons = 82, Neutrons = \( 207 - 82 = 125 \)

2. Table Completion

Emission	Charge	Atomic Symbol	Can Be Stopped By
Beta	\( -1 \)	\( _{-1}^0 e \)	Aluminum foil
Gamma	\( 0 \)	\( \gamma \)	Thick lead or concrete

3. Emission Matching

a) \( \alpha, \beta \)
b) \( \alpha \)
c) \( \alpha \)
d) \( \gamma \)
e) \( \alpha \)
f) \( \beta \)
g) \( \gamma \)

4. Atomic Number Change

a. Alpha decay results in the greatest change (atomic number decreases by 2, while beta changes by 1, gamma by 0).
b. Gamma decay results in the least change (no change in atomic number, as it is energy emission, not a particle with mass/charge that alters \( Z \)).