Nuclear decay occurs according to first-order kinetics. How long will it take for a sample of titanium-45 to decay from 65. 0 grams to 25. 0 grams? the half-life of titanium-45 is 3. 08 hours.

Since radioactive decay is a first-order process, we can also use this equation for the rate constant, which comes from first-order kinetics, which says that the rate constant k is equal to 0.693 divided by the half-life.
Nuclear decay is an excellent example of a first order process. The rate of decay is simply proportional to the amount of the radioactive isotope. This is due to the fact that any isotope has the same chance of decaying at any given time.
Because nuclear decay reactions follow first-order kinetics and have a rate constant that is independent of temperature and the chemical or physical environment, we can perform similar calculations using the half-lives of isotopes to estimate the ages of geological and archaeological artifacts.
The first-order radioactive decay law states that the rate of decay (number of disintegrations per second) is proportional to the number of radioactive atoms (N) present at that time t. N = No e-λt.

#a. ⁵¹₂₂ Ti + ⁰₋₁e → ⁵¹₂₃V

#b. 0.0977 g

#a.

Titanium-51 is the radioisotope that undergoes Beta emission to emit a daughter isotope Vanadium-51 (Mass number-51 and atomic number -23).

Titanium-51 has a mass number of 51 and atomic number of 22.

A beta particle is equivalent to ⁻¹₀e

Beta emission does not affect the mass number of an isotope but increases the atomic number by 1.

Therefore;

The reaction will be;

⁵¹₂₂Ti + ⁻¹₀e → ⁵²₂₂V

#b.

The half life of Ti-51 is 6 minutes

We can calculate the mass remaining after 1 hour (60 min)

Original mass of the sample = 10.0 g

But; using the formula;

Remaining mass = Original mass × (1/2)^n , where n is the number of half lives.

in this case, n = time/half life

= 60 min ÷ 6 min

= 10

Therefore;

Remaining mass = 100 g × (1/2)^10

= 0.0977 g

Therefore, the mass of Ti-51 remaining after 1 hour will be 0.0977 g

To learn more about kinetics refer to:

https://brainly.com/question/13647879

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