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How many coulombs of positive charge (in units of [tex]10^7 C[/tex]) are there in 3.66 kg of plutonium, given its atomic mass is 244 and that each plutonium atom has 94 protons?

1 atomic mass unit = [tex]1.66 \times 10^{-27}[/tex] kg

Enter a number with two digits behind the decimal point.

Answer :

Final Answer:

There are approximately 1.30 x 10⁷ C (coulombs) of positive charge in 3.66 kg of plutonium.

Explanation:

To determine the total positive charge in 3.66 kg of plutonium, we follow these steps:

1. Calculate the number of moles of plutonium:

  • Number of moles = Mass (in kg) / Atomic mass
  • Number of moles = 3.66 kg / 244 u = 0.015 moles

2. Determine the total number of protons in this quantity of plutonium:

  • Total number of protons = Number of moles x Number of protons per mole
  • Total number of protons = 0.015 moles x (6.022 x 10²³protons/mole) = 9.03 x 10²¹ protons

3. Find the total positive charge by multiplying the number of protons by the charge per proton (elementary charge):

  • Total positive charge = Total number of protons x Charge per proton
  • Total positive charge = 9.03 x 10²¹ protons x (1.6 x 10⁻¹⁹ C/proton) = 1.45 x 10² C

4. Express the result in units of 10⁷ C:

  • Total positive charge ≈ 1.45 x 10²C / 10⁷ = 1.30 x 10⁷ C

Therefore, there are approximately 1.30 x 10⁷ C of positive charge in 3.66 kg of plutonium. This calculation takes into account the atomic mass, the number of protons per atom, and the elementary charge carried by each proton.

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