If a reaction yields 2.5165 × 10^8 kJ, then how much mass was lost? (User 3.00 x 108 m/s as the speed of light)
2.30 × 10^-3 kg
5.60 × 10^-3 kg
2.80 × 10^-12 kg
5.60 × 10^-12 kg
Please help.
Its the 3rd choice
To determine how much mass was lost in the reaction, we can use Einstein's mass-energy equivalence equation, which states that energy (E) is equal to mass (m) times the speed of light (c) squared (E = mc^2).
Given:
Energy (E) = 2.5165 × 10^8 kJ = 2.5165 × 10^8 × 1000 J (since 1 kJ = 1000 J)
Speed of light (c) = 3.00 × 10^8 m/s
Substituting these values into the equation:
2.5165 × 10^8 × 1000 J = m × (3.00 × 10^8 m/s)^2
2.5165 × 10^11 J = m × (9.00 × 10^16 m^2/s^2)
Now, we can solve for the mass (m):
m = (2.5165 × 10^11 J) / (9.00 × 10^16 m^2/s^2)
Using scientific notation:
m ≈ 2.80 × 10^-6 kg
Therefore, the mass that was lost in the reaction is approximately 2.80 × 10^-6 kg.
To determine how much mass was lost in the reaction, we can use Einstein's famous equation E = mc^2, where E is the energy released, m is the mass lost, and c is the speed of light.
Given:
Energy released (E) = 2.5165 × 10^8 kJ
Speed of light (c) = 3.00 × 10^8 m/s
First, we need to convert the energy from kilojoules to joules, since the equation uses joules. To do this, we multiply the given energy by 1000:
E = 2.5165 × 10^8 kJ * 1000 = 2.5165 × 10^11 J
Using the equation E = mc^2, we can solve for m (mass lost):
m = E / c^2
Substituting the given values:
m = (2.5165 × 10^11 J) / (3.00 × 10^8 m/s)^2
Simplifying:
m = (2.5165 × 10^11 J) / (9.00 × 10^16 m^2/s^2)
m = 2.7961 × 10^-6 kg
Therefore, the mass lost in the reaction is approximately 2.7961 × 10^-6 kg.
None of the given answer choices match this result exactly. The closest option is 2.80 × 10^-12 kg, but the correct answer should be 2.7961 × 10^-6 kg.
delta E = delta m x c^2
2.5165E11 J = delta m x (3E8)^2
and delta m should come out in kg; BUT I don't see a choice there.