The Richter magnitude scale was developed to assign a number to quantify the magnitude and energy released during an earthquake.
The scale is logarithmic scale of base 10. The magnitude is defined as the logarithm of the ratio of the amplitude of waves measured by a seismograph to an arbitrary small amplitude. An earthquake that measures 5.0 on the Richter scale has a shaking amplitude = 10^ 5/10^4 = 10 times larger than one that measures 4.0.
The given problem describes three major earthquakes as described below:
1. Chilean quake of 1960 had a magnitude of 9.5 in the Richter scale.
2. The Queen Charlotte quake in Canada (1949) had a magnitude of 8.1 in the Richter scale.
3. The strongest ever quake of Canada was in 1700, of magnitude 9.0.
The Chilean quake was therefore, (10^9.5)/(10^8.1)
= 25.12 times bigger.
An earthquake, half as strong as the Queen Charlotte quake referred to above, would thus have a magnitude
= 7.8 (approximately).