Question

Marie Curie is one of the few people to have won two Nobel Prizes and is the subject of a biographical film currently on Amazon. Among her many accomplishments is the discovery of radium-226 (in conjunction with her husband Pierre Curie). Radium-226 (atomic number 88) is an alpha-emitter with a half-life of 1600 years. Suppose you start with 10 units of radium-226. How much will remain after 8000 years? What has happened to the rest of the radium?

Answer 1

After 8000 years, 0.3125 units of radium-226 will remain. The rest of the radium-226 has decayed into other elements through alpha decay.

Step-by-step explanation:

Radium-226 is an alpha-emitter with a half-life of 1600 years. If you start with 10 units of radium-226, after 8000 years, you can calculate the remaining amount using the half-life formula: Remaining amount = Initial amount * (1/2)^(t / half-life), where t is the time in years. Plugging in the values, we have Remaining amount = 10 * (1/2)^(8000 / 1600) = 10 * (1/2)^5 = 10 * 1/32 = 0.3125 units of radium-226 remaining.

As for what has happened to the rest of the radium, over the course of 8000 years, a significant portion of the radium-226 has decayed into other elements through alpha decay. During alpha decay, an alpha particle, consisting of two protons and two neutrons, is emitted from the nucleus of the radium-226 atom. This results in the formation of a new element with a lower atomic number.