Help!
Initially there are 6x10^9 radioactive of element W (decay constant 0.173/day) in a sample. As a nucleus of W decays, it converts 2.67x10^-28 kg of its mass to energy and releases the energy. How much time (in days) is required for the sample to releae a total of 7.2x10^-4J?
0
0.000290
0.00571
0.00943
0.0137
0.0290
0.0571
0.290
0.571
3.29
Please help, I don't even know where to start. :(
To solve this problem, we need to calculate the number of decays that occur and find the corresponding time.
First, let's find the number of decays that would result in the given energy release. The energy released per decay is given as 2.67x10^-28 kg. The total energy released is given as 7.2x10^-4 J.
Number of decays = Total energy released / Energy released per decay
Number of decays = 7.2x10^-4 J / 2.67x10^-28 kg
To simplify the units, we can convert the energy released per decay from kg to J by using Einstein's equation (E = mc^2). The speed of light (c) is approximately 3x10^8 m/s.
Energy released per decay = (2.67x10^-28 kg) * (3x10^8 m/s)^2
Now we can plug in the values and calculate:
Number of decays = (7.2x10^-4 J) / [(2.67x10^-28 kg) * (3x10^8 m/s)^2]
Now, let's determine the total time for these decays to occur. The decay constant for element W is given as 0.173/day. This constant represents the probability of a decay occurring per unit time. Thus, we can use it to find the time for the decays.
Total time = Number of decays / Decay constant
Total time = (Number of decays) / (0.173/day)
Now, let's plug in the value we calculated for the number of decays:
Total time = [(7.2x10^-4 J) / [(2.67x10^-28 kg) * (3x10^8 m/s)^2]] / (0.173/day)
Simplifying this expression will give us the answer in days.
You can input the above equation into a calculator or use a spreadsheet to calculate the total time required for the sample to release the given energy of 7.2x10^-4 J.