Answer:
91.16% has decayed & 8.84% remains
Explanation:
A = A₀e⁻ᵏᵗ => ln(A/A₀) = ln(e⁻ᵏᵗ) => lnA - lnA₀ = -kt => lnA = lnA₀ - kt
Rate Constant (k) = 0.693/half-life = 0.693/10³yrs = 6.93 x 10ˉ⁴yrsˉ¹
Time (t) = 1000yrs
A = fraction of nuclide remaining after 1000yrs
A₀ = original amount of nuclide = 1.00 (= 100%)
lnA = lnA₀ - kt
lnA = ln(1) – (6.93 x 10ˉ⁴yrsˉ¹)(3500yrs) = -2.426
A = eˉ²∙⁴²⁶ = 0.0884 = fraction of nuclide remaining after 3500 years
Amount of nuclide decayed = 1 – 0.0884 = 0.9116 or 91.16% has decayed.
Answer:
2.78 x 10²³
Explanation:
1 mole contains 6.02 x 10²³ hydrogen atoms => 0.46 mole contains 0.46(6.02 x 10²³) hydrogen atoms or 2.78 x 10²³ atoms.
Caution => When to use H vs H₂ => This problem is specific for 'hydrogen atoms' but some may simply say hydrogen. In such cases use H₂ or 'molecular hydrogen' is the focus. it's a matter of semantics, H vs H₂.
![\LARGE{ \boxed{ \rm{ \red{Required \: answer}}}}](https://tex.z-dn.net/?f=%20%5CLARGE%7B%20%5Cboxed%7B%20%20%5Crm%7B%20%5Cred%7BRequired%20%5C%3A%20answer%7D%7D%7D%7D)
☃️ Chemical formulae ➝ ![\sf{CaCO_3}](https://tex.z-dn.net/?f=%5Csf%7BCaCO_3%7D)
<h3>
<u>How to find?</u></h3>
For solving this question, We need to know how to find moles of solution or any substance if a certain weight is given.
![\boxed{ \sf{No. \: of \: moles = \frac{given \: weight}{molecular \: weight} }}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Csf%7BNo.%20%5C%3A%20of%20%5C%3A%20moles%20%3D%20%20%5Cfrac%7Bgiven%20%5C%3A%20weight%7D%7Bmolecular%20%5C%3A%20weight%7D%20%7D%7D)
<h3>
<u>Solution:</u></h3>
Atomic weight of elements:
Ca = 40
C = 12
O = 16
❍ Molecular weight of ![\sf{CaCO_3}](https://tex.z-dn.net/?f=%5Csf%7BCaCO_3%7D)
= 40 + 12 + 3 × 16
= 52 + 48
= 100 g/mol
❍ Given weight: 10 g
Then, no. of moles,
⇛ No. of moles = 10 g / 100 g mol‐¹
⇛ No. of moles = 0.1 moles
☄ No. of moles of Calcium carbonate in that substance = <u>0.1 moles</u>
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