The mass of 900. atoms of sodium(Na)

Chemistry

1 answer:

ivanzaharov [21]2 years ago

7 0

Answer:

3.44 × 10⁻²⁰ g Na

General Formulas and Concepts:

<u>Chemistry - Atomic Structure</u>

Reading a Periodic Table
Using Dimensional Analysis
Avogadro's Number - 6.022 × 10²³ atoms, molecules, formula units, etc.

Explanation:

<u>Step 1: Define</u>

900 atoms Na

<u>Step 2: Identify Conversions</u>

Avogadro's Number

Molar Mass of Na - 22.99 g/mol

<u>Step 3: Convert</u>

<u /> $900 \ atoms \ Na(\frac{1 \ mol \ Na}{6.022 \cdot 10^{23} \ atoms \ Na} )(\frac{22.99 \ g \ Na}{1 \ mol \ Na} )$ = 3.4359 × 10⁻²⁰ g Na

<u>Step 4: Check</u>

<em>We are given 3 sig figs. Follow sig fig rules and round.</em>

3.4359 × 10⁻²⁰ g Na ≈ 3.44 × 10⁻²⁰ g Na

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Uranium-235 decays to form lead-207. The half-life of uranium-235 is 704,000,000 years. What is the approximate age of an igneou

Strike441 [17]

Answer:

The approximate age of the igneous rock is $7.042\times 10^{6}$ years.

Explanation:

Chemically speaking, the Uranium-235 decays to form Lead-207 throughout time. All isotopes decay exponentially by means of the following model:

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$ (1)

In addition, we can determine the time constant of the former isotope in terms of its half life, that is:

$\tau = \frac{t_{1/2}}{\ln 2}$ (2)

Where:

$m_{o}$ - Initial mass of Uranium-235, in atoms.

$m(t)$ - Current mass of Uranium-235, in atoms.

$\tau$ - TIme constant, in years.

$t_{1/2}$ - Half-life of Uranium-235, in years.

Please remind that a 1 : 1 ratio of Uranium-235 to Lead-207 atoms means that current mass of Uranium-235 is a half of its initial mass. If we know that $m(t) = 0.5\cdot m_{o}$ and $t_{1/2} = 7.04\times 10^{8}\,yr$ , then the approximate age of the igneous rock is: