The mass of a hydrogen atom is about 1.67E-24 grams. The mass of a plutonium atom is about 4.05E-22 grams. How many times more grams is an atom of plutonium than an atom of hydrogen?

Question

A.
2.43 × 10-2
B.
2.43 × 102
C.
2.43 × 10-3
D.
2.43 × 103

Answer 1

To find how many times more massive a plutonium atom is compared to a hydrogen atom, we can divide the mass of the plutonium atom by the mass of the hydrogen atom.

Given:

• Mass of a hydrogen atom = \(1.67 \times 10^{-24}\) grams
• Mass of a plutonium atom = \(4.05 \times 10^{-22}\) grams

Now, we can calculate:

\[ \text{Ratio} = \frac{\text{Mass of Plutonium}}{\text{Mass of Hydrogen}} = \frac{4.05 \times 10^{-22}}{1.67 \times 10^{-24}} \]

Calculating this:

1. Divide the coefficients:

\[ \frac{4.05}{1.67} \approx 2.426 \]

2. Subtract the exponents in the powers of ten:

\[ 10^{-22} - (-24) = 10^{-22 + 24} = 10^{2} \]

So, combining these, we have:

\[ \text{Ratio} \approx 2.426 \times 10^{2} \approx 2.43 \times 10^{2} \]

Thus, the answer is:

B. \(2.43 \times 10^{2}\)

Answer 2

A pound of sugar weighs approximately 4.5 × 102 grams. If each grain of sugar weighs 6.25 × 10-4 of a gram, which is the best estimate for the number of grains of sugar in a 5-pound bag?
A.
3.6 × 105 grains
B.
3.6 × 108 grains
C.
3.6 × 106 grains
D.
3.6 × 107 grains

Answer 3

To estimate the number of grains of sugar in a 5-pound bag, we will first calculate the total weight of the sugar in grams and then divide that by the weight of a single grain of sugar.

1. Weight of sugar in a 5-pound bag:

   Since 1 pound of sugar weighs approximately \(4.5 \times 10^{2}\) grams, the weight of a 5-pound bag is:

   \[ \text{Weight of 5 pounds} = 5 \times (4.5 \times 10^{2}) = 22.5 \times 10^{2} \text{ grams} \]

   Simplifying \(22.5 \times 10^{2}\):

   \[ 22.5 \times 10^{2} = 2.25 \times 10^{3} \text{ grams} \]

2. Weight of a single grain of sugar:

   Each grain of sugar weighs \(6.25 \times 10^{-4}\) grams.

3. Calculate the number of grains in the 5-pound bag:

   To find the total number of grains, we can divide the total weight of sugar by the weight of one grain:

   \[ \text{Number of grains} = \frac{2.25 \times 10^{3}}{6.25 \times 10^{-4}} \]

   Dividing the coefficients:

   \[ \frac{2.25}{6.25} = 0.36 \]

   And for the powers of ten:

   \[ 10^{3} - (-4) = 10^{3 + 4} = 10^{7} \]

   Now combining these, we have:

   \[ \text{Number of grains} \approx 0.36 \times 10^{7} = 3.6 \times 10^{6} \]

Thus, the best estimate for the number of grains of sugar in a 5-pound bag is:

C. \(3.6 \times 10^{6}\) grains.