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Correct Answer: an earthquake with a magnitude of 8 on the richter scale releases approximately 32 times as much energy as an earthquake with a magnitude of 7.
an earthquake is a natural phenomenon that occurs due to the sudden release of energy in the earth's lithosphere, which creates seismic waves. these waves can cause the ground to shake, often resulting in noticeable ground movement and potentially causing damage to structures and landscapes. earthquakes can vary widely in size, and scientists use various scales to measure their intensity and the energy they release.
one commonly used scale is the richter scale, developed in the 1930s by charles f. richter. this scale quantifies the size of an earthquake based on the amplitude of the seismic waves recorded by seismographs. importantly, the richter scale is logarithmic, which means that each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release.
this logarithmic nature explains why an earthquake with a magnitude of 8 on the richter scale releases approximately 32 times as much energy as an earthquake with a magnitude of 7. specifically, the energy increase between each consecutive whole number on the richter scale is calculated using the formula \( 10^{1.5 \times (m_2 - m_1)} \), where \( m_1 \) and \( m_2 \) are the magnitudes of the two earthquakes being compared. in the case of comparing magnitudes 7 and 8:
\[ 10^{1.5 \times (8 - 7)} = 10^{1.5} \approx 31.6 \]
this calculation shows that the energy released by an earthquake of magnitude 8 is about 32 times greater than that of a magnitude 7 earthquake.
additionally, the shaking or amplitude of the seismic waves also increases with higher magnitudes on the richter scale, albeit at a different rate. a one-unit increase in magnitude results in approximately ten times the increase in wave amplitude. therefore, an earthquake with a magnitude of 8 would not only release significantly more energy but also result in ten times the ground shaking compared to an earthquake with a magnitude of 7.
understanding these measurements and their implications helps in planning and preparing for seismic events, particularly in regions prone to earthquakes. building codes, emergency response strategies, and public awareness campaigns often rely on data related to earthquake magnitudes and potential energy releases to mitigate damage and enhance public safety.
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