Suppose the atomic mass unit had been defined as 1/10 the average mass of an atom of phosphorus .what would the atomic mass of carbon be on this scale? What would Avogadro's number be ?
To determine the atomic mass of carbon and Avogadro's number on this alternate scale, we'll follow these steps:
1. Find the average mass of an atom of phosphorus:
Since the atomic mass unit is defined as 1/10 the average mass of an atom of phosphorus, we can assume the mass of phosphorus is 10 atomic mass units (AMU).
2. Calculate the atomic mass of carbon:
The atomic mass of carbon is usually 12 AMU on the standard scale. If we assume the atomic mass unit is defined as 1/10 the mass of phosphorus, then the atomic mass of carbon would be (12/10) x 10 = 12 AMU.
3. Determine Avogadro's number:
Avogadro's number represents the number of atoms or molecules in one mole of any substance. On the standard scale, Avogadro's number is approximately 6.022 × 10^23.
If the atomic mass unit were defined as 1/10 the mass of phosphorus, Avogadro's number would remain the same, as it is a fundamental constant in nature.
Therefore, on this scale, the atomic mass of carbon would be 12 AMU, and Avogadro's number would still be approximately 6.022 × 10^23.
To determine the atomic mass of carbon on this scale, we would need to compare it to the atomic mass of phosphorus and use the given information.
Using the new definition that the atomic mass unit (AMU) is 1/10 the average mass of an atom of phosphorus, we consider that the atomic mass of phosphorus would be 10 AMU.
Now, we compare the ratio of the masses of carbon and phosphorus atoms. The current atomic mass of carbon is approximately 12 AMU. Therefore, if the atomic mass of phosphorus is 10 AMU, we can calculate the atomic mass of carbon on this scale using proportion:
(10 AMU) / (12 AMU) = X / (1 AMU)
Cross multiplying:
12 AMU * X = 10 AMU * 1 AMU
X = (10 AMU * 1 AMU) / 12 AMU
Simplifying:
X ≈ 0.83 AMU
So, the atomic mass of carbon would be approximately 0.83 atomic mass units on this new scale.
Next, let's calculate Avogadro's number using this new atomic mass unit.
Avogadro's number, represented as N_A, is defined as the number of entities (atoms, molecules, ions, etc.) present in one mole of a substance. It is currently defined as 6.022 x 10^23.
To determine the new value of Avogadro's number, we need to find the ratio of the current atomic mass unit (AMU) to the new AMU based on phosphorus.
Using the equation:
New AMU / Current AMU = N_A / 6.022 x 10^23
Substituting the values:
1/10 / 1 = N_A / 6.022 x 10^23
Cross multiplying:
N_A = (1/10) * (6.022 x 10^23)
Simplifying:
N_A ≈ 6.022 x 10^22
Therefore, on this new scale, Avogadro's number would be approximately 6.022 x 10^22.