At a relatively close 51.4 kiloparsecs away from the Earth, the supernova of 1987 was the closest nova to occur since telescopes were invented, and it allowed a unique opportunity to confirm that radioactive decay rates are constant over time. Theoretical considerations of the fusion processes in the extreme environment of a supernova blast predict that many isotopes will be created, including a large amount of the short-lived isotope ⁵⁶Co with a half-life of 77.1 days. Figure P30.87 shows the intensity of the light measured from SN1987A as a function of time. A few weeks after the peak intensity, the light from the explosion decays exponentially as a function of time, as one would expect if the light were being generated due to radioactive decay of the created ⁵⁶Co. 

(a) How long ago did the explosion of the supernova take place? 

(b) Using the light curve in Figure P30.87, estimate the half-life of this ⁵⁶Co and compare it with the known half-life. 

(c) Does the result in part (b) suggest that the decay rate of ⁵⁶Co is the same now as it was at the time of the explosion of SN1987A, or does it provide evidence that the decay rate has changed over time?