One of the nuclides in spent nuclear fuel is U-235, an alpha emitter with a half-life of 703 million years. How long will it take for an amount of U-235 to reach 23.0% of its initial amount

1.49 × 10⁹ years

Explanation:

Step 1: Calculate the rate constant (k) for the nuclear decay of U-235

The decay follows first-order kinetics with a half-life (t1/2) of 703 × 10⁶ years. We can calculate "k" using the following expression.

k = ln2/ t1/2 = ln2 / 703 × 10⁶ y = 9.86 × 10⁻¹⁰ y⁻¹

Step 2: Calculate the time elapsed (t) so that the final amount ([U]) is 23.0% of the initial amount ([U]₀)

For first order kinetics, we will use the following expression.

ln ([U]/[U]₀) = -k × t

ln (0.230[U]₀/[U]₀) = -9.86 × 10⁻¹⁰ y⁻¹ × t

ln 0.230 = -9.86 × 10⁻¹⁰ y⁻¹ × t

t = 1.49 × 10⁹ y

when—without warning—something provokes your anger, you may struggle not to succumb to it. since what typically makes you mad is feeling powerless in the face of what seems unfair, your anger is mostly an attempt at a “quick fix” to right the balance. it’s as though you’re raising a fist in protest, proclaiming that you’re not going to capitulate to such injustice.

there are, however, a multitude of problems related to this immediate, push-back reaction of anger. and probably the key one is that almost never does it resolve the issue that gave rise to it. such reactive anger is probably best understood as self-defeating. as david burns, the author of the seminal self- book feeling good, observes: if realistically, acting on your anger is to make any sense, it needs to meet two criteria—which, in almost every case, is frankly impossible. that is, your anger must:

be directed toward a person who has intentionally (and needlessly) behaved in a hurtful way toward you; and

be beneficial or advantageous to you (i.e., assist you in achieving a desired goal).

i think you’ll agree that only rarely can you claim that your anger is both warranted and , whether to yourself or the relationship.

so let me offer you a two-step alternative to abandoning your better judgment and giving in to the temptation of anger—one that should neutralize your anger in seconds. or, when you’re really angry, in minutes.

but keep in mind that you must really want to execute these steps, be sufficiently motivated to perform them. which means overcoming more unconscious resistance than you might ever have imagined. because there are many immediate “advantages” of anger that can interfere with your resolve, i’ll suggest a few of them that might interfere with your employing this powerful method to rid yourself of counter-productive anger.

explanation: