An analytical laboratory balance typically measures mass to the nearest 0.1 mg. What energy change would accompany the loss of 0.1 mg in mass, according to Einstein's mass-energy equivalence principle (E=mc²)?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

검증된 단계별 안내

Step 1: Identify the given values. The mass loss \( \Delta m \) is 0.1 mg, which needs to be converted to kilograms for use in the equation. Remember that 1 mg = 1 \(\times\) 10^{-3} \) g and 1 g = 1 \(\times\) 10^{-3} \) kg.

Step 2: Convert the mass loss from milligrams to kilograms. Use the conversion factors to find \( \Delta m \) in kg.

Step 3: Recall Einstein's mass-energy equivalence principle, which is given by the equation \( E = mc^2 \), where \( E \) is the energy, \( m \) is the mass, and \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s).

Step 4: Substitute the converted mass \( \Delta m \) and the speed of light \( c \) into the equation \( E = mc^2 \) to calculate the energy change \( E \).

Step 5: Perform the multiplication to find the energy change \( E \) in joules, keeping track of the units to ensure they are consistent.

주요 개념

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Mass-Energy Equivalence

Mass-energy equivalence is a principle formulated by Albert Einstein, expressed by the equation E=mc², which states that mass (m) can be converted into energy (E) and vice versa. In this equation, c represents the speed of light in a vacuum, a constant that indicates the immense amount of energy contained in even a small amount of mass. This principle is fundamental in understanding nuclear reactions and the energy produced in processes like fusion and fission.

Analytical Balance

An analytical balance is a highly sensitive instrument used in laboratories to measure mass with great precision, often to the nearest 0.1 mg or better. It operates on the principle of electromagnetic force restoration, where the mass of the sample is balanced against a known force. The accuracy of these balances is crucial in quantitative analysis, as even minute differences in mass can significantly affect experimental results and calculations.

Energy Change Calculation

To calculate the energy change associated with a mass loss using the mass-energy equivalence principle, one can substitute the mass value into the equation E=mc². For a mass loss of 0.1 mg (or 0.0001 g), this involves converting grams to kilograms (0.0001 g = 1.0 x 10^-7 kg) and then multiplying by the square of the speed of light (approximately 3.00 x 10^8 m/s). This calculation reveals the energy released or absorbed due to the change in mass, illustrating the profound relationship between mass and energy.