Question

1. naturally occurring europium (eu) consists of two isotopes with a mass of 151 and 153. europium-151 has an abundance of 48.03% and europium-153 has an abundance of 51.97%. what is the atomic mass of europium? 10. strontium consists of four isotopes with masses of 84 (abundance 0.50%), 86 (abundance of 9.9%), 87 (abundance of 7.0%), and 88 (abundance of 82.6%). calculate the atomic mass of strontium.

Explanation:

Problem 9: Atomic Mass of Europium

Step 1: Recall the formula for atomic mass

The atomic mass of an element is the weighted average of the masses of its isotopes, calculated as:
$$\text{Atomic Mass} = (m_1 \times f_1) + (m_2 \times f_2)$$
where \( m \) is the mass of the isotope and \( f \) is its fractional abundance.

Step 2: Convert abundances to fractions

Europium - 151: \( f_1 = \frac{48.03}{100} = 0.4803 \), \( m_1 = 151 \)
Europium - 153: \( f_2 = \frac{51.97}{100} = 0.5197 \), \( m_2 = 153 \)

Step 3: Calculate the weighted sum

$$\text{Atomic Mass} = (151 \times 0.4803) + (153 \times 0.5197)$$
First, calculate \( 151 \times 0.4803 \approx 72.5253 \)
Then, calculate \( 153 \times 0.5197 \approx 79.5141 \)
Add the two results: \( 72.5253 + 79.5141 \approx 152.0394 \)

Problem 10: Atomic Mass of Strontium

Step 1: Recall the formula for atomic mass

The atomic mass of an element is the weighted average of the masses of its isotopes, calculated as:
$$\text{Atomic Mass} = (m_1 \times f_1) + (m_2 \times f_2) + (m_3 \times f_3) + (m_4 \times f_4)$$
where \( m \) is the mass of the isotope and \( f \) is its fractional abundance.

Step 2: Convert abundances to fractions

Strontium - 84: \( f_1 = \frac{0.50}{100} = 0.005 \), \( m_1 = 84 \)
Strontium - 86: \( f_2 = \frac{9.9}{100} = 0.099 \), \( m_2 = 86 \)
Strontium - 87: \( f_3 = \frac{7.0}{100} = 0.07 \), \( m_3 = 87 \)
Strontium - 88: \( f_4 = \frac{82.6}{100} = 0.826 \), \( m_4 = 88 \)

Step 3: Calculate the weighted sum

$$\text{Atomic Mass} = (84 \times 0.005) + (86 \times 0.099) + (87 \times 0.07) + (88 \times 0.826)$$

• \( 84 \times 0.005 = 0.42 \)
• \( 86 \times 0.099 = 8.514 \)
• \( 87 \times 0.07 = 6.09 \)
• \( 88 \times 0.826 = 72.688 \)

Add the results: \( 0.42 + 8.514 + 6.09 + 72.688 = 87.712 \)

Answer:

s:

• Europium Atomic Mass: \(\approx 152.04\) (or more precisely \(152.04\) when rounded appropriately)
• Strontium Atomic Mass: \(87.712\) (or \(87.71\) when rounded to two decimal places)