Beryllium-7 (
) is produced in the upper atmosphere and then sinks down onto the Earth’s surface. Nuclei of beryllium-7 decay with a half-life of 53.3 days to form stable nuclei. The activity of a sample of beryllium-7 on a tree leaf is 
.
Show that the decay constant of beryllium-7 is 
.
Determine the mass of the beryllium-7 on the leaf.
The leaf is covered so that no further beryllium-7 is added to the existing sample from the atmosphere. Calculate the time that must elapse before the activity of the sample is reduced to 
.
.
.
