2. Cesium -137 has a half-life of about 30 years. If we b with 200 mg of cesium -137 , will it take more or less the 230 years until only 1 milligram remains?

To determine how long it will take for 200 mg of cesium-137 to decay to 1 mg, we can use the concept of half-life.<br /><br />The half-life of cesium-137 is 30 years. This means that every 30 years, the amount of cesium-137 will be reduced by half.<br /><br />Let's calculate the number of half-lives it takes for 200 mg to decay to 1 mg:<br /><br />1. After 1 half-life (30 years), 200 mg will decay to 100 mg.<br />2. After 2 half-lives (60 years), 100 mg will decay to 50 mg.<br />3. After 3 half-lives (90 years), 50 mg will decay to 25 mg.<br />4. After 4 half-lives (120 years), 25 mg will decay to 12.5 mg.<br />5. After 5 half-lives (150 years), 12.5 mg will decay to 6.25 mg.<br />6. After 6 half-lives (180 years), 6.25 mg will decay to 3.125 mg.<br />7. After 7 half-lives (210 years), 3.125 mg will decay to 1.5625 mg.<br />8. After 8 half-lives (240 years), 1.5625 mg will decay to 0.78125 mg.<br /><br />Since we want to find out when the amount of cesium-137 will be reduced to 1 mg, we need to consider the next half-life:<br /><br />9. After 9 half-lives (270 years), 0.78125 mg will decay to 0.390625 mg.<br />10. After 10 half-lives (300 years), 0.390625 mg will decay to 0.1953125 mg.<br /><br />Therefore, it will take approximately 10 half-lives, or 300 years, for 200 mg of cesium-137 to decay to 1 mg.