Is the length of time required for one-half of an isotope to decay?

Is the length of time required for one-half of an isotope to decay?

An interesting and useful aspect of radioactive decay is half-life, which is the amount of time it takes for one-half of a radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by coTnditions and is independent of the initial amount of that isotope.

What is the time it takes for half of the nuclei to decay called?

Half-life: The half life ( T1/2 ) of a radioactive element is the time it takes for half of the nuclei to decay (either convert to another element or become an isotope of the same element).

What is radioactive decay equation?

The radioactive decay law states that the probability per unit time that a nucleus will decay is a constant, independent of time. The radioactive decay of certain number of atoms (mass) is exponential in time. Radioactive decay law: N = N.e-λt. The rate of nuclear decay is also measured in terms of half-lives.

Why is phosphorus 32 unstable?

The nucleus of phosphorus-32 contains 15 protons and 17 neutrons, one more neutron than the most common isotope of phosphorus, phosphorus-31. Phosphorus-32 only exists in small quantities on Earth as it has a short half-life of 14.268 days and so decays rapidly.

What is the use of phosphorus 32?

Phosphorus-32 (also known as P-32) treatment uses a radioactive form of sodium phosphate. Because P-32 is radioactive, it can be used to treat some diseases by injecting it into the body. When P-32 is injected into the bloodstream it collects in the bone marrow where it slows down the production of new blood cells.

Is Phosphorus a stable element?

White phosphorus exists in two crystalline forms: α (alpha) and β (beta). At room temperature, the α-form is stable, which is more common and it has cubic crystal structure and at 195.2 K (−78.0 °C), it transforms into β-form, which has hexagonal crystal structure.

What is the half-life of phosphorus 32?

14.3 days

How does P 32 decay?

Phosphorus 32 (P-32) is the phosphorus isotope whose nucleus consists of 15 protons and 17 neutrons. It disintegrates by emitting a β- (1.71 MeV) particle in 32S with a half-life of 14.263 days. It is an artificial radioactive substance obtained by neutron bombardment of stable phosphorus.

How do you calculate the half-life of phosphorus 32?

The half-life of phosphorus-32 is 14.26 days. The decay constant is k = 4.86 x 10−2 decays/day.

What fraction of the original amount of phosphorus 32 remains after 3 half-lives?

Q: What fraction of the original amount of phosphorus-32 remains after three half-lives? A: After three half-lives, or 42 days, 1/8 (1/2 × 1/2 × 1/2) of the original amount of phosphorus-32 remains.

What is the fraction equivalent of 3 half-lives?


Number of half-lives elapsed Fraction remaining Percentage remaining
3 1⁄8 .5
4 1⁄16 .25
5 1⁄32 .125
6 1⁄64 .5625

How do half-lives work?

Half-life is used to describe exponential decay. In one half-life period, on average, half of the C14 atoms would decay. So one would expect that if you start with four C14 atoms, you would after one half life have two, and after another half life only one would remain.

What is the half life of the sample?

Half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive …

What is the half-life of a radioactive substance?

The half-life of a radioactive substance is a characteristic constant. It measures the time it takes for a given amount of the substance to become reduced by half as a consequence of decay, and therefore, the emission of radiation.

Why is half life important?

Understanding the concept of half-life is useful for determining excretion rates as well as steady-state concentrations for any specific drug. Different drugs have different half-lives; however, they all follow this rule: after one half-life has passed, 50% of the initial drug amount is removed from the body.

What is relation between half life and mean life?

It turns out that the mean life equals the half life divided by the natural logarithm of 2 (about 0.693). The mean life also turns out to exactly equal the number τ that appears in the exponential term e−t/τ involved with describing decay or growth, called the time constant.

What does half life mean?

What Is Half-Life? A medication’s biological half-life refers simply to how long it takes for half of the dose to be metabolized and eliminated from the bloodstream. Or, put another way, the half-life of a drug is the time it takes for it to be reduced by half.

What is the average life of a radioactive element?

7.2 min

What is the relationship between Half Life and radioactivity?

This shows that the population decays exponentially at a rate that depends on the decay constant. The time required for half of the original population of radioactive atoms to decay is called the half-life. The relationship between the half-life, T1/2, and the decay constant is given by T1/2 = 0.693/λ.

What is half life and average life?

Note that the radioactive half-life is not the same as the average lifetime, the half-life being 0.693 times the average lifetime. The example that causes the most confusion is the decay of the free neutron with a half-life of 10.3 minutes and an average lifetime of 14.9 minutes.

What affects the half-life of a radioactive element?

The half-life of a radioactive material can be changed using time dilation effects. According to relativity, time itself can be slowed down. Everything that experiences time can therefore be given a longer effective lifetime if time is dilated.