Answer:
To determine the magnitude of an earthquake that is one-half as intense as the earthquake with a magnitude of 8.0, we can use the logarithmic scale of earthquake magnitudes.
The magnitude of an earthquake is based on the logarithm of the amplitude of seismic waves recorded by seismographs. The scale is logarithmic, which means that each whole number increase in magnitude represents a tenfold increase in the amplitude of the seismic waves and approximately 31.6 times more energy release.
To find an earthquake that is one-half as intense, we need to find the magnitude that represents a seismic wave amplitude half that of the magnitude 8.0 earthquake.
Using the logarithmic scale, we can express this as:
Magnitude - Magnitude of the earthquake = log10(Amplitude / Amplitude of the earthquake)
Since we want an earthquake half as intense, the amplitude ratio will be 1/2:
Magnitude - 8.0 = log10(1/2)
Solving for magnitude:
Magnitude = 8.0 + log10(1/2)
Using logarithm properties, we can simplify the expression:
Magnitude ≈ 8.0 - 0.3
Magnitude ≈ 7.7
Therefore, an earthquake that is one-half as intense as the earthquake with a magnitude of 8.0 would have a magnitude of approximately 7.7 to the nearest tenth.