How much decay occurs for Ga-67 over a period of 27 hours?

Gallium-67 has a half-life of approximately 78 hours. To determine how much decay occurs over a 27-hour period, you can use the concept of half-lives and the decay formula.

The decay formula can be expressed mathematically as:

[ N(t) = N_0 \times \left( \frac{1}{2} \right)^{t/T_{\frac{1}{2}}} ]

Where:

• ( N(t) ) is the remaining quantity after time ( t )

• ( N_0 ) is the initial quantity

• ( t ) is the time elapsed

• ( T_{\frac{1}{2}} ) is the half-life

In this scenario, after 27 hours, one would calculate how many half-lives fit into that time frame. Since 27 hours is less than one-half of the 78-hour half-life, there will be some decay, but only a fraction of a half-life has passed. The decay factor can be computed by determining:

[ \text{Decay Factor} = \left( \frac{1}{2} \right)^{27/78} ]

Using this calculation, you can deduce the remaining